% TIMEFORMAT='%3R'; { time (exec 2>&1; /home/martin/bin/satallax -E /home/martin/.isabelle/contrib/e-2.5-1/x86_64-linux/eprover -p tstp -t 5 /home/martin/judgement-day/tptp-thf/tptp/Hoare/prob_442__3254746_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:14:55.877

% Could-be-implicit typings (11)
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thf(ty_n_t__Hoare____Mirabelle____raqjowkjvm__Otriple_It__Com__Ostate_J, type,
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thf(ty_n_t__Set__Oset_It__Set__Oset_It__Com__Opname_J_J, type,
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thf(ty_n_t__Option__Ooption_It__Com__Ocom_J, type,
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thf(ty_n_t__Set__Oset_It__Com__Opname_J, type,
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thf(ty_n_t__Com__Ostate, type,
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thf(ty_n_t__Com__Opname, type,
    pname : $tType).
thf(ty_n_t__Com__Ocom, type,
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% Explicit typings (53)
thf(sy_c_Com_OWT, type,
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thf(sy_c_Com_OWT__bodies, type,
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thf(sy_c_Com_Obody, type,
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thf(sy_c_Set_Oimage_001t__Com__Opname_001t__Com__Opname, type,
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thf(sy_c_Set_Oimage_001t__Com__Opname_001t__Hoare____Mirabelle____raqjowkjvm__Otriple_It__Com__Ostate_J, type,
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thf(sy_c_Set_Oimage_001t__Com__Opname_001t__Set__Oset_It__Hoare____Mirabelle____raqjowkjvm__Otriple_It__Com__Ostate_J_J, type,
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thf(sy_c_Set_Oimage_001t__Hoare____Mirabelle____raqjowkjvm__Otriple_It__Com__Ostate_J_001t__Com__Opname, type,
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thf(sy_c_Set_Oimage_001t__Hoare____Mirabelle____raqjowkjvm__Otriple_It__Com__Ostate_J_001t__Hoare____Mirabelle____raqjowkjvm__Otriple_It__Com__Ostate_J, type,
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thf(sy_c_Set_Oimage_001t__Hoare____Mirabelle____raqjowkjvm__Otriple_It__Com__Ostate_J_001t__Set__Oset_It__Com__Opname_J, type,
    image_222083648_pname : (hoare_958474565_state > set_pname) > set_Ho840737317_state > set_set_pname).
thf(sy_c_Set_Oimage_001t__Hoare____Mirabelle____raqjowkjvm__Otriple_It__Com__Ostate_J_001t__Set__Oset_It__Hoare____Mirabelle____raqjowkjvm__Otriple_It__Com__Ostate_J_J, type,
    image_1038902228_state : (hoare_958474565_state > set_Ho840737317_state) > set_Ho840737317_state > set_se421025541_state).
thf(sy_c_Set_Oimage_001t__Set__Oset_It__Com__Opname_J_001t__Com__Opname, type,
    image_1672683217_pname : (set_pname > pname) > set_set_pname > set_pname).
thf(sy_c_Set_Oimage_001t__Set__Oset_It__Com__Opname_J_001t__Hoare____Mirabelle____raqjowkjvm__Otriple_It__Com__Ostate_J, type,
    image_800262846_state : (set_pname > hoare_958474565_state) > set_set_pname > set_Ho840737317_state).
thf(sy_c_Set_Oimage_001t__Set__Oset_It__Com__Opname_J_001t__Set__Oset_It__Com__Opname_J, type,
    image_1068293127_pname : (set_pname > set_pname) > set_set_pname > set_set_pname).
thf(sy_c_Set_Oimage_001t__Set__Oset_It__Com__Opname_J_001t__Set__Oset_It__Hoare____Mirabelle____raqjowkjvm__Otriple_It__Com__Ostate_J_J, type,
    image_434380702_state : (set_pname > set_Ho840737317_state) > set_set_pname > set_se421025541_state).
thf(sy_c_Set_Oimage_001t__Set__Oset_It__Hoare____Mirabelle____raqjowkjvm__Otriple_It__Com__Ostate_J_J_001t__Com__Opname, type,
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    image_1207908734_state : (set_Ho840737317_state > hoare_958474565_state) > set_se421025541_state > set_Ho840737317_state).
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    image_2095143712_pname : (set_Ho840737317_state > set_pname) > set_se421025541_state > set_set_pname).
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    image_565609652_state : (set_Ho840737317_state > set_Ho840737317_state) > set_se421025541_state > set_se421025541_state).
thf(sy_c_Set_Oinsert_001t__Com__Opname, type,
    insert_pname : pname > set_pname > set_pname).
thf(sy_c_Set_Oinsert_001t__Hoare____Mirabelle____raqjowkjvm__Otriple_It__Com__Ostate_J, type,
    insert776267541_state : hoare_958474565_state > set_Ho840737317_state > set_Ho840737317_state).
thf(sy_c_Set_Oinsert_001t__Set__Oset_It__Com__Opname_J, type,
    insert_set_pname : set_pname > set_set_pname > set_set_pname).
thf(sy_c_Set_Oinsert_001t__Set__Oset_It__Hoare____Mirabelle____raqjowkjvm__Otriple_It__Com__Ostate_J_J, type,
    insert1860247541_state : set_Ho840737317_state > set_se421025541_state > set_se421025541_state).
thf(sy_c_member_001t__Com__Opname, type,
    member_pname : pname > set_pname > $o).
thf(sy_c_member_001t__Hoare____Mirabelle____raqjowkjvm__Otriple_It__Com__Ostate_J, type,
    member109514606_state : hoare_958474565_state > set_Ho840737317_state > $o).
thf(sy_c_member_001t__Set__Oset_It__Com__Opname_J, type,
    member_set_pname : set_pname > set_set_pname > $o).
thf(sy_c_member_001t__Set__Oset_It__Hoare____Mirabelle____raqjowkjvm__Otriple_It__Com__Ostate_J_J, type,
    member1959617614_state : set_Ho840737317_state > set_se421025541_state > $o).
thf(sy_v_Fa, type,
    fa : set_Ho840737317_state).
thf(sy_v_x, type,
    x : hoare_958474565_state).

% Relevant facts (248)
thf(fact_0_thin, axiom,
    ((![G : set_Ho840737317_state, Ts : set_Ho840737317_state, G2 : set_Ho840737317_state]: ((hoare_604442164_state @ G @ Ts) => ((ord_le1945819589_state @ G @ G2) => (hoare_604442164_state @ G2 @ Ts)))))). % thin
thf(fact_1_single__stateE, axiom,
    ((hoare_405891322gleton => (![T : state]: (~ ((![S : state]: (S = T)))))))). % single_stateE
thf(fact_2_asm, axiom,
    ((![Ts : set_Ho840737317_state, G2 : set_Ho840737317_state]: ((ord_le1945819589_state @ Ts @ G2) => (hoare_604442164_state @ G2 @ Ts))))). % asm
thf(fact_3_cut, axiom,
    ((![G : set_Ho840737317_state, Ts : set_Ho840737317_state, G2 : set_Ho840737317_state]: ((hoare_604442164_state @ G @ Ts) => ((hoare_604442164_state @ G2 @ G) => (hoare_604442164_state @ G2 @ Ts)))))). % cut
thf(fact_4_weaken, axiom,
    ((![G2 : set_Ho840737317_state, Ts2 : set_Ho840737317_state, Ts : set_Ho840737317_state]: ((hoare_604442164_state @ G2 @ Ts2) => ((ord_le1945819589_state @ Ts @ Ts2) => (hoare_604442164_state @ G2 @ Ts)))))). % weaken
thf(fact_5_state__not__singleton__def, axiom,
    ((hoare_405891322gleton = (?[S2 : state]: (?[T2 : state]: (~ ((S2 = T2)))))))). % state_not_singleton_def
thf(fact_6_finite__Collect__subsets, axiom,
    ((![A : set_se421025541_state]: ((finite1266962254_state @ A) => (finite1160699950_state @ (collec1927138160_state @ (^[B : set_se421025541_state]: (ord_le1363676837_state @ B @ A)))))))). % finite_Collect_subsets
thf(fact_7_finite__Collect__subsets, axiom,
    ((![A : set_set_pname]: ((finite505202775_pname @ A) => (finite1638948493_pname @ (collec2100311499_pname @ (^[B : set_set_pname]: (ord_le2066558166_pname @ B @ A)))))))). % finite_Collect_subsets
thf(fact_8_finite__Collect__subsets, axiom,
    ((![A : set_pname]: ((finite_finite_pname @ A) => (finite505202775_pname @ (collect_set_pname @ (^[B : set_pname]: (ord_le865024672_pname @ B @ A)))))))). % finite_Collect_subsets
thf(fact_9_finite__Collect__subsets, axiom,
    ((![A : set_Ho840737317_state]: ((finite1986656878_state @ A) => (finite1266962254_state @ (collec305218192_state @ (^[B : set_Ho840737317_state]: (ord_le1945819589_state @ B @ A)))))))). % finite_Collect_subsets
thf(fact_10_insert__subset, axiom,
    ((![X : pname, A : set_pname, B2 : set_pname]: ((ord_le865024672_pname @ (insert_pname @ X @ A) @ B2) = (((member_pname @ X @ B2)) & ((ord_le865024672_pname @ A @ B2))))))). % insert_subset
thf(fact_11_insert__subset, axiom,
    ((![X : hoare_958474565_state, A : set_Ho840737317_state, B2 : set_Ho840737317_state]: ((ord_le1945819589_state @ (insert776267541_state @ X @ A) @ B2) = (((member109514606_state @ X @ B2)) & ((ord_le1945819589_state @ A @ B2))))))). % insert_subset
thf(fact_12_finite__insert, axiom,
    ((![A2 : set_Ho840737317_state, A : set_se421025541_state]: ((finite1266962254_state @ (insert1860247541_state @ A2 @ A)) = (finite1266962254_state @ A))))). % finite_insert
thf(fact_13_finite__insert, axiom,
    ((![A2 : set_pname, A : set_set_pname]: ((finite505202775_pname @ (insert_set_pname @ A2 @ A)) = (finite505202775_pname @ A))))). % finite_insert
thf(fact_14_finite__insert, axiom,
    ((![A2 : hoare_958474565_state, A : set_Ho840737317_state]: ((finite1986656878_state @ (insert776267541_state @ A2 @ A)) = (finite1986656878_state @ A))))). % finite_insert
thf(fact_15_finite__insert, axiom,
    ((![A2 : pname, A : set_pname]: ((finite_finite_pname @ (insert_pname @ A2 @ A)) = (finite_finite_pname @ A))))). % finite_insert
thf(fact_16_image__insert, axiom,
    ((![F : hoare_958474565_state > pname, A2 : hoare_958474565_state, B2 : set_Ho840737317_state]: ((image_871391498_pname @ F @ (insert776267541_state @ A2 @ B2)) = (insert_pname @ (F @ A2) @ (image_871391498_pname @ F @ B2)))))). % image_insert
thf(fact_17_image__insert, axiom,
    ((![F : pname > pname, A2 : pname, B2 : set_pname]: ((image_pname_pname @ F @ (insert_pname @ A2 @ B2)) = (insert_pname @ (F @ A2) @ (image_pname_pname @ F @ B2)))))). % image_insert
thf(fact_18_image__insert, axiom,
    ((![F : pname > hoare_958474565_state, A2 : pname, B2 : set_pname]: ((image_2144627828_state @ F @ (insert_pname @ A2 @ B2)) = (insert776267541_state @ (F @ A2) @ (image_2144627828_state @ F @ B2)))))). % image_insert
thf(fact_19_image__insert, axiom,
    ((![F : hoare_958474565_state > hoare_958474565_state, A2 : hoare_958474565_state, B2 : set_Ho840737317_state]: ((image_1849792670_state @ F @ (insert776267541_state @ A2 @ B2)) = (insert776267541_state @ (F @ A2) @ (image_1849792670_state @ F @ B2)))))). % image_insert
thf(fact_20_insert__image, axiom,
    ((![X : pname, A : set_pname, F : pname > hoare_958474565_state]: ((member_pname @ X @ A) => ((insert776267541_state @ (F @ X) @ (image_2144627828_state @ F @ A)) = (image_2144627828_state @ F @ A)))))). % insert_image
thf(fact_21_insert__image, axiom,
    ((![X : hoare_958474565_state, A : set_Ho840737317_state, F : hoare_958474565_state > hoare_958474565_state]: ((member109514606_state @ X @ A) => ((insert776267541_state @ (F @ X) @ (image_1849792670_state @ F @ A)) = (image_1849792670_state @ F @ A)))))). % insert_image
thf(fact_22_insert__image, axiom,
    ((![X : hoare_958474565_state, A : set_Ho840737317_state, F : hoare_958474565_state > pname]: ((member109514606_state @ X @ A) => ((insert_pname @ (F @ X) @ (image_871391498_pname @ F @ A)) = (image_871391498_pname @ F @ A)))))). % insert_image
thf(fact_23_finite__imageI, axiom,
    ((![F2 : set_pname, H : pname > pname]: ((finite_finite_pname @ F2) => (finite_finite_pname @ (image_pname_pname @ H @ F2)))))). % finite_imageI
thf(fact_24_finite__imageI, axiom,
    ((![F2 : set_Ho840737317_state, H : hoare_958474565_state > pname]: ((finite1986656878_state @ F2) => (finite_finite_pname @ (image_871391498_pname @ H @ F2)))))). % finite_imageI
thf(fact_25_finite__imageI, axiom,
    ((![F2 : set_pname, H : pname > hoare_958474565_state]: ((finite_finite_pname @ F2) => (finite1986656878_state @ (image_2144627828_state @ H @ F2)))))). % finite_imageI
thf(fact_26_finite__imageI, axiom,
    ((![F2 : set_pname, H : pname > set_pname]: ((finite_finite_pname @ F2) => (finite505202775_pname @ (image_747505105_pname @ H @ F2)))))). % finite_imageI
thf(fact_27_finite__imageI, axiom,
    ((![F2 : set_set_pname, H : set_pname > pname]: ((finite505202775_pname @ F2) => (finite_finite_pname @ (image_1672683217_pname @ H @ F2)))))). % finite_imageI
thf(fact_28_finite__imageI, axiom,
    ((![F2 : set_Ho840737317_state, H : hoare_958474565_state > hoare_958474565_state]: ((finite1986656878_state @ F2) => (finite1986656878_state @ (image_1849792670_state @ H @ F2)))))). % finite_imageI
thf(fact_29_finite__imageI, axiom,
    ((![F2 : set_Ho840737317_state, H : hoare_958474565_state > set_pname]: ((finite1986656878_state @ F2) => (finite505202775_pname @ (image_222083648_pname @ H @ F2)))))). % finite_imageI
thf(fact_30_finite__imageI, axiom,
    ((![F2 : set_pname, H : pname > set_Ho840737317_state]: ((finite_finite_pname @ F2) => (finite1266962254_state @ (image_1030990164_state @ H @ F2)))))). % finite_imageI
thf(fact_31_finite__imageI, axiom,
    ((![F2 : set_se421025541_state, H : set_Ho840737317_state > pname]: ((finite1266962254_state @ F2) => (finite_finite_pname @ (image_1133019626_pname @ H @ F2)))))). % finite_imageI
thf(fact_32_finite__imageI, axiom,
    ((![F2 : set_set_pname, H : set_pname > hoare_958474565_state]: ((finite505202775_pname @ F2) => (finite1986656878_state @ (image_800262846_state @ H @ F2)))))). % finite_imageI
thf(fact_33_finite__Collect__conjI, axiom,
    ((![P : hoare_958474565_state > $o, Q : hoare_958474565_state > $o]: (((finite1986656878_state @ (collec305460656_state @ P)) | (finite1986656878_state @ (collec305460656_state @ Q))) => (finite1986656878_state @ (collec305460656_state @ (^[X2 : hoare_958474565_state]: (((P @ X2)) & ((Q @ X2)))))))))). % finite_Collect_conjI
thf(fact_34_finite__Collect__conjI, axiom,
    ((![P : pname > $o, Q : pname > $o]: (((finite_finite_pname @ (collect_pname @ P)) | (finite_finite_pname @ (collect_pname @ Q))) => (finite_finite_pname @ (collect_pname @ (^[X2 : pname]: (((P @ X2)) & ((Q @ X2)))))))))). % finite_Collect_conjI
thf(fact_35_finite__Collect__conjI, axiom,
    ((![P : set_Ho840737317_state > $o, Q : set_Ho840737317_state > $o]: (((finite1266962254_state @ (collec305218192_state @ P)) | (finite1266962254_state @ (collec305218192_state @ Q))) => (finite1266962254_state @ (collec305218192_state @ (^[X2 : set_Ho840737317_state]: (((P @ X2)) & ((Q @ X2)))))))))). % finite_Collect_conjI
thf(fact_36_finite__Collect__conjI, axiom,
    ((![P : set_pname > $o, Q : set_pname > $o]: (((finite505202775_pname @ (collect_set_pname @ P)) | (finite505202775_pname @ (collect_set_pname @ Q))) => (finite505202775_pname @ (collect_set_pname @ (^[X2 : set_pname]: (((P @ X2)) & ((Q @ X2)))))))))). % finite_Collect_conjI
thf(fact_37_finite__Collect__disjI, axiom,
    ((![P : hoare_958474565_state > $o, Q : hoare_958474565_state > $o]: ((finite1986656878_state @ (collec305460656_state @ (^[X2 : hoare_958474565_state]: (((P @ X2)) | ((Q @ X2)))))) = (((finite1986656878_state @ (collec305460656_state @ P))) & ((finite1986656878_state @ (collec305460656_state @ Q)))))))). % finite_Collect_disjI
thf(fact_38_finite__Collect__disjI, axiom,
    ((![P : pname > $o, Q : pname > $o]: ((finite_finite_pname @ (collect_pname @ (^[X2 : pname]: (((P @ X2)) | ((Q @ X2)))))) = (((finite_finite_pname @ (collect_pname @ P))) & ((finite_finite_pname @ (collect_pname @ Q)))))))). % finite_Collect_disjI
thf(fact_39_finite__Collect__disjI, axiom,
    ((![P : set_Ho840737317_state > $o, Q : set_Ho840737317_state > $o]: ((finite1266962254_state @ (collec305218192_state @ (^[X2 : set_Ho840737317_state]: (((P @ X2)) | ((Q @ X2)))))) = (((finite1266962254_state @ (collec305218192_state @ P))) & ((finite1266962254_state @ (collec305218192_state @ Q)))))))). % finite_Collect_disjI
thf(fact_40_finite__Collect__disjI, axiom,
    ((![P : set_pname > $o, Q : set_pname > $o]: ((finite505202775_pname @ (collect_set_pname @ (^[X2 : set_pname]: (((P @ X2)) | ((Q @ X2)))))) = (((finite505202775_pname @ (collect_set_pname @ P))) & ((finite505202775_pname @ (collect_set_pname @ Q)))))))). % finite_Collect_disjI
thf(fact_41_image__ident, axiom,
    ((![Y : set_Ho840737317_state]: ((image_1849792670_state @ (^[X2 : hoare_958474565_state]: X2) @ Y) = Y)))). % image_ident
thf(fact_42_finite__surj, axiom,
    ((![A : set_pname, B2 : set_pname, F : pname > pname]: ((finite_finite_pname @ A) => ((ord_le865024672_pname @ B2 @ (image_pname_pname @ F @ A)) => (finite_finite_pname @ B2)))))). % finite_surj
thf(fact_43_finite__surj, axiom,
    ((![A : set_pname, B2 : set_set_pname, F : pname > set_pname]: ((finite_finite_pname @ A) => ((ord_le2066558166_pname @ B2 @ (image_747505105_pname @ F @ A)) => (finite505202775_pname @ B2)))))). % finite_surj
thf(fact_44_finite__surj, axiom,
    ((![A : set_pname, B2 : set_Ho840737317_state, F : pname > hoare_958474565_state]: ((finite_finite_pname @ A) => ((ord_le1945819589_state @ B2 @ (image_2144627828_state @ F @ A)) => (finite1986656878_state @ B2)))))). % finite_surj
thf(fact_45_finite__surj, axiom,
    ((![A : set_Ho840737317_state, B2 : set_pname, F : hoare_958474565_state > pname]: ((finite1986656878_state @ A) => ((ord_le865024672_pname @ B2 @ (image_871391498_pname @ F @ A)) => (finite_finite_pname @ B2)))))). % finite_surj
thf(fact_46_finite__surj, axiom,
    ((![A : set_set_pname, B2 : set_pname, F : set_pname > pname]: ((finite505202775_pname @ A) => ((ord_le865024672_pname @ B2 @ (image_1672683217_pname @ F @ A)) => (finite_finite_pname @ B2)))))). % finite_surj
thf(fact_47_finite__surj, axiom,
    ((![A : set_Ho840737317_state, B2 : set_set_pname, F : hoare_958474565_state > set_pname]: ((finite1986656878_state @ A) => ((ord_le2066558166_pname @ B2 @ (image_222083648_pname @ F @ A)) => (finite505202775_pname @ B2)))))). % finite_surj
thf(fact_48_finite__surj, axiom,
    ((![A : set_pname, B2 : set_se421025541_state, F : pname > set_Ho840737317_state]: ((finite_finite_pname @ A) => ((ord_le1363676837_state @ B2 @ (image_1030990164_state @ F @ A)) => (finite1266962254_state @ B2)))))). % finite_surj
thf(fact_49_finite__surj, axiom,
    ((![A : set_set_pname, B2 : set_set_pname, F : set_pname > set_pname]: ((finite505202775_pname @ A) => ((ord_le2066558166_pname @ B2 @ (image_1068293127_pname @ F @ A)) => (finite505202775_pname @ B2)))))). % finite_surj
thf(fact_50_finite__surj, axiom,
    ((![A : set_Ho840737317_state, B2 : set_Ho840737317_state, F : hoare_958474565_state > hoare_958474565_state]: ((finite1986656878_state @ A) => ((ord_le1945819589_state @ B2 @ (image_1849792670_state @ F @ A)) => (finite1986656878_state @ B2)))))). % finite_surj
thf(fact_51_finite__surj, axiom,
    ((![A : set_set_pname, B2 : set_Ho840737317_state, F : set_pname > hoare_958474565_state]: ((finite505202775_pname @ A) => ((ord_le1945819589_state @ B2 @ (image_800262846_state @ F @ A)) => (finite1986656878_state @ B2)))))). % finite_surj
thf(fact_52_finite__subset__image, axiom,
    ((![B2 : set_pname, F : pname > pname, A : set_pname]: ((finite_finite_pname @ B2) => ((ord_le865024672_pname @ B2 @ (image_pname_pname @ F @ A)) => (?[C : set_pname]: ((ord_le865024672_pname @ C @ A) & ((finite_finite_pname @ C) & (B2 = (image_pname_pname @ F @ C)))))))))). % finite_subset_image
thf(fact_53_finite__subset__image, axiom,
    ((![B2 : set_set_pname, F : pname > set_pname, A : set_pname]: ((finite505202775_pname @ B2) => ((ord_le2066558166_pname @ B2 @ (image_747505105_pname @ F @ A)) => (?[C : set_pname]: ((ord_le865024672_pname @ C @ A) & ((finite_finite_pname @ C) & (B2 = (image_747505105_pname @ F @ C)))))))))). % finite_subset_image
thf(fact_54_finite__subset__image, axiom,
    ((![B2 : set_Ho840737317_state, F : pname > hoare_958474565_state, A : set_pname]: ((finite1986656878_state @ B2) => ((ord_le1945819589_state @ B2 @ (image_2144627828_state @ F @ A)) => (?[C : set_pname]: ((ord_le865024672_pname @ C @ A) & ((finite_finite_pname @ C) & (B2 = (image_2144627828_state @ F @ C)))))))))). % finite_subset_image
thf(fact_55_finite__subset__image, axiom,
    ((![B2 : set_pname, F : set_pname > pname, A : set_set_pname]: ((finite_finite_pname @ B2) => ((ord_le865024672_pname @ B2 @ (image_1672683217_pname @ F @ A)) => (?[C : set_set_pname]: ((ord_le2066558166_pname @ C @ A) & ((finite505202775_pname @ C) & (B2 = (image_1672683217_pname @ F @ C)))))))))). % finite_subset_image
thf(fact_56_finite__subset__image, axiom,
    ((![B2 : set_pname, F : hoare_958474565_state > pname, A : set_Ho840737317_state]: ((finite_finite_pname @ B2) => ((ord_le865024672_pname @ B2 @ (image_871391498_pname @ F @ A)) => (?[C : set_Ho840737317_state]: ((ord_le1945819589_state @ C @ A) & ((finite1986656878_state @ C) & (B2 = (image_871391498_pname @ F @ C)))))))))). % finite_subset_image
thf(fact_57_finite__subset__image, axiom,
    ((![B2 : set_set_pname, F : set_pname > set_pname, A : set_set_pname]: ((finite505202775_pname @ B2) => ((ord_le2066558166_pname @ B2 @ (image_1068293127_pname @ F @ A)) => (?[C : set_set_pname]: ((ord_le2066558166_pname @ C @ A) & ((finite505202775_pname @ C) & (B2 = (image_1068293127_pname @ F @ C)))))))))). % finite_subset_image
thf(fact_58_finite__subset__image, axiom,
    ((![B2 : set_set_pname, F : hoare_958474565_state > set_pname, A : set_Ho840737317_state]: ((finite505202775_pname @ B2) => ((ord_le2066558166_pname @ B2 @ (image_222083648_pname @ F @ A)) => (?[C : set_Ho840737317_state]: ((ord_le1945819589_state @ C @ A) & ((finite1986656878_state @ C) & (B2 = (image_222083648_pname @ F @ C)))))))))). % finite_subset_image
thf(fact_59_finite__subset__image, axiom,
    ((![B2 : set_se421025541_state, F : pname > set_Ho840737317_state, A : set_pname]: ((finite1266962254_state @ B2) => ((ord_le1363676837_state @ B2 @ (image_1030990164_state @ F @ A)) => (?[C : set_pname]: ((ord_le865024672_pname @ C @ A) & ((finite_finite_pname @ C) & (B2 = (image_1030990164_state @ F @ C)))))))))). % finite_subset_image
thf(fact_60_finite__subset__image, axiom,
    ((![B2 : set_Ho840737317_state, F : set_pname > hoare_958474565_state, A : set_set_pname]: ((finite1986656878_state @ B2) => ((ord_le1945819589_state @ B2 @ (image_800262846_state @ F @ A)) => (?[C : set_set_pname]: ((ord_le2066558166_pname @ C @ A) & ((finite505202775_pname @ C) & (B2 = (image_800262846_state @ F @ C)))))))))). % finite_subset_image
thf(fact_61_finite__subset__image, axiom,
    ((![B2 : set_Ho840737317_state, F : hoare_958474565_state > hoare_958474565_state, A : set_Ho840737317_state]: ((finite1986656878_state @ B2) => ((ord_le1945819589_state @ B2 @ (image_1849792670_state @ F @ A)) => (?[C : set_Ho840737317_state]: ((ord_le1945819589_state @ C @ A) & ((finite1986656878_state @ C) & (B2 = (image_1849792670_state @ F @ C)))))))))). % finite_subset_image
thf(fact_62_ex__finite__subset__image, axiom,
    ((![F : pname > pname, A : set_pname, P : set_pname > $o]: ((?[B : set_pname]: (((finite_finite_pname @ B)) & ((((ord_le865024672_pname @ B @ (image_pname_pname @ F @ A))) & ((P @ B)))))) = (?[B : set_pname]: (((finite_finite_pname @ B)) & ((((ord_le865024672_pname @ B @ A)) & ((P @ (image_pname_pname @ F @ B))))))))))). % ex_finite_subset_image
thf(fact_63_ex__finite__subset__image, axiom,
    ((![F : pname > set_pname, A : set_pname, P : set_set_pname > $o]: ((?[B : set_set_pname]: (((finite505202775_pname @ B)) & ((((ord_le2066558166_pname @ B @ (image_747505105_pname @ F @ A))) & ((P @ B)))))) = (?[B : set_pname]: (((finite_finite_pname @ B)) & ((((ord_le865024672_pname @ B @ A)) & ((P @ (image_747505105_pname @ F @ B))))))))))). % ex_finite_subset_image
thf(fact_64_ex__finite__subset__image, axiom,
    ((![F : pname > hoare_958474565_state, A : set_pname, P : set_Ho840737317_state > $o]: ((?[B : set_Ho840737317_state]: (((finite1986656878_state @ B)) & ((((ord_le1945819589_state @ B @ (image_2144627828_state @ F @ A))) & ((P @ B)))))) = (?[B : set_pname]: (((finite_finite_pname @ B)) & ((((ord_le865024672_pname @ B @ A)) & ((P @ (image_2144627828_state @ F @ B))))))))))). % ex_finite_subset_image
thf(fact_65_ex__finite__subset__image, axiom,
    ((![F : set_pname > pname, A : set_set_pname, P : set_pname > $o]: ((?[B : set_pname]: (((finite_finite_pname @ B)) & ((((ord_le865024672_pname @ B @ (image_1672683217_pname @ F @ A))) & ((P @ B)))))) = (?[B : set_set_pname]: (((finite505202775_pname @ B)) & ((((ord_le2066558166_pname @ B @ A)) & ((P @ (image_1672683217_pname @ F @ B))))))))))). % ex_finite_subset_image
thf(fact_66_ex__finite__subset__image, axiom,
    ((![F : hoare_958474565_state > pname, A : set_Ho840737317_state, P : set_pname > $o]: ((?[B : set_pname]: (((finite_finite_pname @ B)) & ((((ord_le865024672_pname @ B @ (image_871391498_pname @ F @ A))) & ((P @ B)))))) = (?[B : set_Ho840737317_state]: (((finite1986656878_state @ B)) & ((((ord_le1945819589_state @ B @ A)) & ((P @ (image_871391498_pname @ F @ B))))))))))). % ex_finite_subset_image
thf(fact_67_ex__finite__subset__image, axiom,
    ((![F : set_pname > set_pname, A : set_set_pname, P : set_set_pname > $o]: ((?[B : set_set_pname]: (((finite505202775_pname @ B)) & ((((ord_le2066558166_pname @ B @ (image_1068293127_pname @ F @ A))) & ((P @ B)))))) = (?[B : set_set_pname]: (((finite505202775_pname @ B)) & ((((ord_le2066558166_pname @ B @ A)) & ((P @ (image_1068293127_pname @ F @ B))))))))))). % ex_finite_subset_image
thf(fact_68_ex__finite__subset__image, axiom,
    ((![F : hoare_958474565_state > set_pname, A : set_Ho840737317_state, P : set_set_pname > $o]: ((?[B : set_set_pname]: (((finite505202775_pname @ B)) & ((((ord_le2066558166_pname @ B @ (image_222083648_pname @ F @ A))) & ((P @ B)))))) = (?[B : set_Ho840737317_state]: (((finite1986656878_state @ B)) & ((((ord_le1945819589_state @ B @ A)) & ((P @ (image_222083648_pname @ F @ B))))))))))). % ex_finite_subset_image
thf(fact_69_ex__finite__subset__image, axiom,
    ((![F : pname > set_Ho840737317_state, A : set_pname, P : set_se421025541_state > $o]: ((?[B : set_se421025541_state]: (((finite1266962254_state @ B)) & ((((ord_le1363676837_state @ B @ (image_1030990164_state @ F @ A))) & ((P @ B)))))) = (?[B : set_pname]: (((finite_finite_pname @ B)) & ((((ord_le865024672_pname @ B @ A)) & ((P @ (image_1030990164_state @ F @ B))))))))))). % ex_finite_subset_image
thf(fact_70_ex__finite__subset__image, axiom,
    ((![F : set_pname > hoare_958474565_state, A : set_set_pname, P : set_Ho840737317_state > $o]: ((?[B : set_Ho840737317_state]: (((finite1986656878_state @ B)) & ((((ord_le1945819589_state @ B @ (image_800262846_state @ F @ A))) & ((P @ B)))))) = (?[B : set_set_pname]: (((finite505202775_pname @ B)) & ((((ord_le2066558166_pname @ B @ A)) & ((P @ (image_800262846_state @ F @ B))))))))))). % ex_finite_subset_image
thf(fact_71_ex__finite__subset__image, axiom,
    ((![F : hoare_958474565_state > hoare_958474565_state, A : set_Ho840737317_state, P : set_Ho840737317_state > $o]: ((?[B : set_Ho840737317_state]: (((finite1986656878_state @ B)) & ((((ord_le1945819589_state @ B @ (image_1849792670_state @ F @ A))) & ((P @ B)))))) = (?[B : set_Ho840737317_state]: (((finite1986656878_state @ B)) & ((((ord_le1945819589_state @ B @ A)) & ((P @ (image_1849792670_state @ F @ B))))))))))). % ex_finite_subset_image
thf(fact_72_image__eqI, axiom,
    ((![B3 : hoare_958474565_state, F : pname > hoare_958474565_state, X : pname, A : set_pname]: ((B3 = (F @ X)) => ((member_pname @ X @ A) => (member109514606_state @ B3 @ (image_2144627828_state @ F @ A))))))). % image_eqI
thf(fact_73_image__eqI, axiom,
    ((![B3 : hoare_958474565_state, F : hoare_958474565_state > hoare_958474565_state, X : hoare_958474565_state, A : set_Ho840737317_state]: ((B3 = (F @ X)) => ((member109514606_state @ X @ A) => (member109514606_state @ B3 @ (image_1849792670_state @ F @ A))))))). % image_eqI
thf(fact_74_subset__antisym, axiom,
    ((![A : set_Ho840737317_state, B2 : set_Ho840737317_state]: ((ord_le1945819589_state @ A @ B2) => ((ord_le1945819589_state @ B2 @ A) => (A = B2)))))). % subset_antisym
thf(fact_75_subset__antisym, axiom,
    ((![A : set_pname, B2 : set_pname]: ((ord_le865024672_pname @ A @ B2) => ((ord_le865024672_pname @ B2 @ A) => (A = B2)))))). % subset_antisym
thf(fact_76_subsetI, axiom,
    ((![A : set_Ho840737317_state, B2 : set_Ho840737317_state]: ((![X3 : hoare_958474565_state]: ((member109514606_state @ X3 @ A) => (member109514606_state @ X3 @ B2))) => (ord_le1945819589_state @ A @ B2))))). % subsetI
thf(fact_77_subsetI, axiom,
    ((![A : set_pname, B2 : set_pname]: ((![X3 : pname]: ((member_pname @ X3 @ A) => (member_pname @ X3 @ B2))) => (ord_le865024672_pname @ A @ B2))))). % subsetI
thf(fact_78_insert__absorb2, axiom,
    ((![X : hoare_958474565_state, A : set_Ho840737317_state]: ((insert776267541_state @ X @ (insert776267541_state @ X @ A)) = (insert776267541_state @ X @ A))))). % insert_absorb2
thf(fact_79_insert__absorb2, axiom,
    ((![X : pname, A : set_pname]: ((insert_pname @ X @ (insert_pname @ X @ A)) = (insert_pname @ X @ A))))). % insert_absorb2
thf(fact_80_insert__iff, axiom,
    ((![A2 : pname, B3 : pname, A : set_pname]: ((member_pname @ A2 @ (insert_pname @ B3 @ A)) = (((A2 = B3)) | ((member_pname @ A2 @ A))))))). % insert_iff
thf(fact_81_insert__iff, axiom,
    ((![A2 : hoare_958474565_state, B3 : hoare_958474565_state, A : set_Ho840737317_state]: ((member109514606_state @ A2 @ (insert776267541_state @ B3 @ A)) = (((A2 = B3)) | ((member109514606_state @ A2 @ A))))))). % insert_iff
thf(fact_82_insertCI, axiom,
    ((![A2 : pname, B2 : set_pname, B3 : pname]: (((~ ((member_pname @ A2 @ B2))) => (A2 = B3)) => (member_pname @ A2 @ (insert_pname @ B3 @ B2)))))). % insertCI
thf(fact_83_insertCI, axiom,
    ((![A2 : hoare_958474565_state, B2 : set_Ho840737317_state, B3 : hoare_958474565_state]: (((~ ((member109514606_state @ A2 @ B2))) => (A2 = B3)) => (member109514606_state @ A2 @ (insert776267541_state @ B3 @ B2)))))). % insertCI
thf(fact_84_rev__image__eqI, axiom,
    ((![X : pname, A : set_pname, B3 : hoare_958474565_state, F : pname > hoare_958474565_state]: ((member_pname @ X @ A) => ((B3 = (F @ X)) => (member109514606_state @ B3 @ (image_2144627828_state @ F @ A))))))). % rev_image_eqI
thf(fact_85_rev__image__eqI, axiom,
    ((![X : hoare_958474565_state, A : set_Ho840737317_state, B3 : hoare_958474565_state, F : hoare_958474565_state > hoare_958474565_state]: ((member109514606_state @ X @ A) => ((B3 = (F @ X)) => (member109514606_state @ B3 @ (image_1849792670_state @ F @ A))))))). % rev_image_eqI
thf(fact_86_ball__imageD, axiom,
    ((![F : pname > hoare_958474565_state, A : set_pname, P : hoare_958474565_state > $o]: ((![X3 : hoare_958474565_state]: ((member109514606_state @ X3 @ (image_2144627828_state @ F @ A)) => (P @ X3))) => (![X4 : pname]: ((member_pname @ X4 @ A) => (P @ (F @ X4)))))))). % ball_imageD
thf(fact_87_ball__imageD, axiom,
    ((![F : hoare_958474565_state > hoare_958474565_state, A : set_Ho840737317_state, P : hoare_958474565_state > $o]: ((![X3 : hoare_958474565_state]: ((member109514606_state @ X3 @ (image_1849792670_state @ F @ A)) => (P @ X3))) => (![X4 : hoare_958474565_state]: ((member109514606_state @ X4 @ A) => (P @ (F @ X4)))))))). % ball_imageD
thf(fact_88_image__cong, axiom,
    ((![M : set_pname, N : set_pname, F : pname > hoare_958474565_state, G3 : pname > hoare_958474565_state]: ((M = N) => ((![X3 : pname]: ((member_pname @ X3 @ N) => ((F @ X3) = (G3 @ X3)))) => ((image_2144627828_state @ F @ M) = (image_2144627828_state @ G3 @ N))))))). % image_cong
thf(fact_89_image__cong, axiom,
    ((![M : set_Ho840737317_state, N : set_Ho840737317_state, F : hoare_958474565_state > hoare_958474565_state, G3 : hoare_958474565_state > hoare_958474565_state]: ((M = N) => ((![X3 : hoare_958474565_state]: ((member109514606_state @ X3 @ N) => ((F @ X3) = (G3 @ X3)))) => ((image_1849792670_state @ F @ M) = (image_1849792670_state @ G3 @ N))))))). % image_cong
thf(fact_90_bex__imageD, axiom,
    ((![F : pname > hoare_958474565_state, A : set_pname, P : hoare_958474565_state > $o]: ((?[X4 : hoare_958474565_state]: ((member109514606_state @ X4 @ (image_2144627828_state @ F @ A)) & (P @ X4))) => (?[X3 : pname]: ((member_pname @ X3 @ A) & (P @ (F @ X3)))))))). % bex_imageD
thf(fact_91_bex__imageD, axiom,
    ((![F : hoare_958474565_state > hoare_958474565_state, A : set_Ho840737317_state, P : hoare_958474565_state > $o]: ((?[X4 : hoare_958474565_state]: ((member109514606_state @ X4 @ (image_1849792670_state @ F @ A)) & (P @ X4))) => (?[X3 : hoare_958474565_state]: ((member109514606_state @ X3 @ A) & (P @ (F @ X3)))))))). % bex_imageD
thf(fact_92_image__iff, axiom,
    ((![Z : hoare_958474565_state, F : pname > hoare_958474565_state, A : set_pname]: ((member109514606_state @ Z @ (image_2144627828_state @ F @ A)) = (?[X2 : pname]: (((member_pname @ X2 @ A)) & ((Z = (F @ X2))))))))). % image_iff
thf(fact_93_image__iff, axiom,
    ((![Z : hoare_958474565_state, F : hoare_958474565_state > hoare_958474565_state, A : set_Ho840737317_state]: ((member109514606_state @ Z @ (image_1849792670_state @ F @ A)) = (?[X2 : hoare_958474565_state]: (((member109514606_state @ X2 @ A)) & ((Z = (F @ X2))))))))). % image_iff
thf(fact_94_imageI, axiom,
    ((![X : pname, A : set_pname, F : pname > hoare_958474565_state]: ((member_pname @ X @ A) => (member109514606_state @ (F @ X) @ (image_2144627828_state @ F @ A)))))). % imageI
thf(fact_95_imageI, axiom,
    ((![X : hoare_958474565_state, A : set_Ho840737317_state, F : hoare_958474565_state > hoare_958474565_state]: ((member109514606_state @ X @ A) => (member109514606_state @ (F @ X) @ (image_1849792670_state @ F @ A)))))). % imageI
thf(fact_96_Collect__mono__iff, axiom,
    ((![P : set_Ho840737317_state > $o, Q : set_Ho840737317_state > $o]: ((ord_le1363676837_state @ (collec305218192_state @ P) @ (collec305218192_state @ Q)) = (![X2 : set_Ho840737317_state]: (((P @ X2)) => ((Q @ X2)))))))). % Collect_mono_iff
thf(fact_97_Collect__mono__iff, axiom,
    ((![P : set_pname > $o, Q : set_pname > $o]: ((ord_le2066558166_pname @ (collect_set_pname @ P) @ (collect_set_pname @ Q)) = (![X2 : set_pname]: (((P @ X2)) => ((Q @ X2)))))))). % Collect_mono_iff
thf(fact_98_Collect__mono__iff, axiom,
    ((![P : hoare_958474565_state > $o, Q : hoare_958474565_state > $o]: ((ord_le1945819589_state @ (collec305460656_state @ P) @ (collec305460656_state @ Q)) = (![X2 : hoare_958474565_state]: (((P @ X2)) => ((Q @ X2)))))))). % Collect_mono_iff
thf(fact_99_Collect__mono__iff, axiom,
    ((![P : pname > $o, Q : pname > $o]: ((ord_le865024672_pname @ (collect_pname @ P) @ (collect_pname @ Q)) = (![X2 : pname]: (((P @ X2)) => ((Q @ X2)))))))). % Collect_mono_iff
thf(fact_100_set__eq__subset, axiom,
    (((^[Y2 : set_Ho840737317_state]: (^[Z2 : set_Ho840737317_state]: (Y2 = Z2))) = (^[A3 : set_Ho840737317_state]: (^[B : set_Ho840737317_state]: (((ord_le1945819589_state @ A3 @ B)) & ((ord_le1945819589_state @ B @ A3)))))))). % set_eq_subset
thf(fact_101_set__eq__subset, axiom,
    (((^[Y2 : set_pname]: (^[Z2 : set_pname]: (Y2 = Z2))) = (^[A3 : set_pname]: (^[B : set_pname]: (((ord_le865024672_pname @ A3 @ B)) & ((ord_le865024672_pname @ B @ A3)))))))). % set_eq_subset
thf(fact_102_subset__trans, axiom,
    ((![A : set_Ho840737317_state, B2 : set_Ho840737317_state, C2 : set_Ho840737317_state]: ((ord_le1945819589_state @ A @ B2) => ((ord_le1945819589_state @ B2 @ C2) => (ord_le1945819589_state @ A @ C2)))))). % subset_trans
thf(fact_103_subset__trans, axiom,
    ((![A : set_pname, B2 : set_pname, C2 : set_pname]: ((ord_le865024672_pname @ A @ B2) => ((ord_le865024672_pname @ B2 @ C2) => (ord_le865024672_pname @ A @ C2)))))). % subset_trans
thf(fact_104_Collect__mono, axiom,
    ((![P : set_Ho840737317_state > $o, Q : set_Ho840737317_state > $o]: ((![X3 : set_Ho840737317_state]: ((P @ X3) => (Q @ X3))) => (ord_le1363676837_state @ (collec305218192_state @ P) @ (collec305218192_state @ Q)))))). % Collect_mono
thf(fact_105_Collect__mono, axiom,
    ((![P : set_pname > $o, Q : set_pname > $o]: ((![X3 : set_pname]: ((P @ X3) => (Q @ X3))) => (ord_le2066558166_pname @ (collect_set_pname @ P) @ (collect_set_pname @ Q)))))). % Collect_mono
thf(fact_106_Collect__mono, axiom,
    ((![P : hoare_958474565_state > $o, Q : hoare_958474565_state > $o]: ((![X3 : hoare_958474565_state]: ((P @ X3) => (Q @ X3))) => (ord_le1945819589_state @ (collec305460656_state @ P) @ (collec305460656_state @ Q)))))). % Collect_mono
thf(fact_107_Collect__mono, axiom,
    ((![P : pname > $o, Q : pname > $o]: ((![X3 : pname]: ((P @ X3) => (Q @ X3))) => (ord_le865024672_pname @ (collect_pname @ P) @ (collect_pname @ Q)))))). % Collect_mono
thf(fact_108_subset__refl, axiom,
    ((![A : set_Ho840737317_state]: (ord_le1945819589_state @ A @ A)))). % subset_refl
thf(fact_109_subset__refl, axiom,
    ((![A : set_pname]: (ord_le865024672_pname @ A @ A)))). % subset_refl
thf(fact_110_subset__iff, axiom,
    ((ord_le1945819589_state = (^[A3 : set_Ho840737317_state]: (^[B : set_Ho840737317_state]: (![T2 : hoare_958474565_state]: (((member109514606_state @ T2 @ A3)) => ((member109514606_state @ T2 @ B))))))))). % subset_iff
thf(fact_111_subset__iff, axiom,
    ((ord_le865024672_pname = (^[A3 : set_pname]: (^[B : set_pname]: (![T2 : pname]: (((member_pname @ T2 @ A3)) => ((member_pname @ T2 @ B))))))))). % subset_iff
thf(fact_112_equalityD2, axiom,
    ((![A : set_Ho840737317_state, B2 : set_Ho840737317_state]: ((A = B2) => (ord_le1945819589_state @ B2 @ A))))). % equalityD2
thf(fact_113_equalityD2, axiom,
    ((![A : set_pname, B2 : set_pname]: ((A = B2) => (ord_le865024672_pname @ B2 @ A))))). % equalityD2
thf(fact_114_equalityD1, axiom,
    ((![A : set_Ho840737317_state, B2 : set_Ho840737317_state]: ((A = B2) => (ord_le1945819589_state @ A @ B2))))). % equalityD1
thf(fact_115_equalityD1, axiom,
    ((![A : set_pname, B2 : set_pname]: ((A = B2) => (ord_le865024672_pname @ A @ B2))))). % equalityD1
thf(fact_116_subset__eq, axiom,
    ((ord_le1945819589_state = (^[A3 : set_Ho840737317_state]: (^[B : set_Ho840737317_state]: (![X2 : hoare_958474565_state]: (((member109514606_state @ X2 @ A3)) => ((member109514606_state @ X2 @ B))))))))). % subset_eq
thf(fact_117_subset__eq, axiom,
    ((ord_le865024672_pname = (^[A3 : set_pname]: (^[B : set_pname]: (![X2 : pname]: (((member_pname @ X2 @ A3)) => ((member_pname @ X2 @ B))))))))). % subset_eq
thf(fact_118_equalityE, axiom,
    ((![A : set_Ho840737317_state, B2 : set_Ho840737317_state]: ((A = B2) => (~ (((ord_le1945819589_state @ A @ B2) => (~ ((ord_le1945819589_state @ B2 @ A)))))))))). % equalityE
thf(fact_119_equalityE, axiom,
    ((![A : set_pname, B2 : set_pname]: ((A = B2) => (~ (((ord_le865024672_pname @ A @ B2) => (~ ((ord_le865024672_pname @ B2 @ A)))))))))). % equalityE
thf(fact_120_subsetD, axiom,
    ((![A : set_Ho840737317_state, B2 : set_Ho840737317_state, C3 : hoare_958474565_state]: ((ord_le1945819589_state @ A @ B2) => ((member109514606_state @ C3 @ A) => (member109514606_state @ C3 @ B2)))))). % subsetD
thf(fact_121_subsetD, axiom,
    ((![A : set_pname, B2 : set_pname, C3 : pname]: ((ord_le865024672_pname @ A @ B2) => ((member_pname @ C3 @ A) => (member_pname @ C3 @ B2)))))). % subsetD
thf(fact_122_in__mono, axiom,
    ((![A : set_Ho840737317_state, B2 : set_Ho840737317_state, X : hoare_958474565_state]: ((ord_le1945819589_state @ A @ B2) => ((member109514606_state @ X @ A) => (member109514606_state @ X @ B2)))))). % in_mono
thf(fact_123_in__mono, axiom,
    ((![A : set_pname, B2 : set_pname, X : pname]: ((ord_le865024672_pname @ A @ B2) => ((member_pname @ X @ A) => (member_pname @ X @ B2)))))). % in_mono
thf(fact_124_mem__Collect__eq, axiom,
    ((![A2 : hoare_958474565_state, P : hoare_958474565_state > $o]: ((member109514606_state @ A2 @ (collec305460656_state @ P)) = (P @ A2))))). % mem_Collect_eq
thf(fact_125_mem__Collect__eq, axiom,
    ((![A2 : set_Ho840737317_state, P : set_Ho840737317_state > $o]: ((member1959617614_state @ A2 @ (collec305218192_state @ P)) = (P @ A2))))). % mem_Collect_eq
thf(fact_126_mem__Collect__eq, axiom,
    ((![A2 : set_pname, P : set_pname > $o]: ((member_set_pname @ A2 @ (collect_set_pname @ P)) = (P @ A2))))). % mem_Collect_eq
thf(fact_127_Collect__mem__eq, axiom,
    ((![A : set_Ho840737317_state]: ((collec305460656_state @ (^[X2 : hoare_958474565_state]: (member109514606_state @ X2 @ A))) = A)))). % Collect_mem_eq
thf(fact_128_Collect__mem__eq, axiom,
    ((![A : set_se421025541_state]: ((collec305218192_state @ (^[X2 : set_Ho840737317_state]: (member1959617614_state @ X2 @ A))) = A)))). % Collect_mem_eq
thf(fact_129_Collect__mem__eq, axiom,
    ((![A : set_set_pname]: ((collect_set_pname @ (^[X2 : set_pname]: (member_set_pname @ X2 @ A))) = A)))). % Collect_mem_eq
thf(fact_130_Collect__cong, axiom,
    ((![P : set_Ho840737317_state > $o, Q : set_Ho840737317_state > $o]: ((![X3 : set_Ho840737317_state]: ((P @ X3) = (Q @ X3))) => ((collec305218192_state @ P) = (collec305218192_state @ Q)))))). % Collect_cong
thf(fact_131_Collect__cong, axiom,
    ((![P : set_pname > $o, Q : set_pname > $o]: ((![X3 : set_pname]: ((P @ X3) = (Q @ X3))) => ((collect_set_pname @ P) = (collect_set_pname @ Q)))))). % Collect_cong
thf(fact_132_mk__disjoint__insert, axiom,
    ((![A2 : pname, A : set_pname]: ((member_pname @ A2 @ A) => (?[B4 : set_pname]: ((A = (insert_pname @ A2 @ B4)) & (~ ((member_pname @ A2 @ B4))))))))). % mk_disjoint_insert
thf(fact_133_mk__disjoint__insert, axiom,
    ((![A2 : hoare_958474565_state, A : set_Ho840737317_state]: ((member109514606_state @ A2 @ A) => (?[B4 : set_Ho840737317_state]: ((A = (insert776267541_state @ A2 @ B4)) & (~ ((member109514606_state @ A2 @ B4))))))))). % mk_disjoint_insert
thf(fact_134_insert__commute, axiom,
    ((![X : hoare_958474565_state, Y3 : hoare_958474565_state, A : set_Ho840737317_state]: ((insert776267541_state @ X @ (insert776267541_state @ Y3 @ A)) = (insert776267541_state @ Y3 @ (insert776267541_state @ X @ A)))))). % insert_commute
thf(fact_135_insert__commute, axiom,
    ((![X : pname, Y3 : pname, A : set_pname]: ((insert_pname @ X @ (insert_pname @ Y3 @ A)) = (insert_pname @ Y3 @ (insert_pname @ X @ A)))))). % insert_commute
thf(fact_136_insert__eq__iff, axiom,
    ((![A2 : pname, A : set_pname, B3 : pname, B2 : set_pname]: ((~ ((member_pname @ A2 @ A))) => ((~ ((member_pname @ B3 @ B2))) => (((insert_pname @ A2 @ A) = (insert_pname @ B3 @ B2)) = (((((A2 = B3)) => ((A = B2)))) & ((((~ ((A2 = B3)))) => ((?[C4 : set_pname]: (((A = (insert_pname @ B3 @ C4))) & ((((~ ((member_pname @ B3 @ C4)))) & ((((B2 = (insert_pname @ A2 @ C4))) & ((~ ((member_pname @ A2 @ C4)))))))))))))))))))). % insert_eq_iff
thf(fact_137_insert__eq__iff, axiom,
    ((![A2 : hoare_958474565_state, A : set_Ho840737317_state, B3 : hoare_958474565_state, B2 : set_Ho840737317_state]: ((~ ((member109514606_state @ A2 @ A))) => ((~ ((member109514606_state @ B3 @ B2))) => (((insert776267541_state @ A2 @ A) = (insert776267541_state @ B3 @ B2)) = (((((A2 = B3)) => ((A = B2)))) & ((((~ ((A2 = B3)))) => ((?[C4 : set_Ho840737317_state]: (((A = (insert776267541_state @ B3 @ C4))) & ((((~ ((member109514606_state @ B3 @ C4)))) & ((((B2 = (insert776267541_state @ A2 @ C4))) & ((~ ((member109514606_state @ A2 @ C4)))))))))))))))))))). % insert_eq_iff
thf(fact_138_insert__absorb, axiom,
    ((![A2 : pname, A : set_pname]: ((member_pname @ A2 @ A) => ((insert_pname @ A2 @ A) = A))))). % insert_absorb
thf(fact_139_insert__absorb, axiom,
    ((![A2 : hoare_958474565_state, A : set_Ho840737317_state]: ((member109514606_state @ A2 @ A) => ((insert776267541_state @ A2 @ A) = A))))). % insert_absorb
thf(fact_140_insert__ident, axiom,
    ((![X : pname, A : set_pname, B2 : set_pname]: ((~ ((member_pname @ X @ A))) => ((~ ((member_pname @ X @ B2))) => (((insert_pname @ X @ A) = (insert_pname @ X @ B2)) = (A = B2))))))). % insert_ident
thf(fact_141_insert__ident, axiom,
    ((![X : hoare_958474565_state, A : set_Ho840737317_state, B2 : set_Ho840737317_state]: ((~ ((member109514606_state @ X @ A))) => ((~ ((member109514606_state @ X @ B2))) => (((insert776267541_state @ X @ A) = (insert776267541_state @ X @ B2)) = (A = B2))))))). % insert_ident
thf(fact_142_Set_Oset__insert, axiom,
    ((![X : pname, A : set_pname]: ((member_pname @ X @ A) => (~ ((![B4 : set_pname]: ((A = (insert_pname @ X @ B4)) => (member_pname @ X @ B4))))))))). % Set.set_insert
thf(fact_143_Set_Oset__insert, axiom,
    ((![X : hoare_958474565_state, A : set_Ho840737317_state]: ((member109514606_state @ X @ A) => (~ ((![B4 : set_Ho840737317_state]: ((A = (insert776267541_state @ X @ B4)) => (member109514606_state @ X @ B4))))))))). % Set.set_insert
thf(fact_144_insertI2, axiom,
    ((![A2 : pname, B2 : set_pname, B3 : pname]: ((member_pname @ A2 @ B2) => (member_pname @ A2 @ (insert_pname @ B3 @ B2)))))). % insertI2
thf(fact_145_insertI2, axiom,
    ((![A2 : hoare_958474565_state, B2 : set_Ho840737317_state, B3 : hoare_958474565_state]: ((member109514606_state @ A2 @ B2) => (member109514606_state @ A2 @ (insert776267541_state @ B3 @ B2)))))). % insertI2
thf(fact_146_insertI1, axiom,
    ((![A2 : pname, B2 : set_pname]: (member_pname @ A2 @ (insert_pname @ A2 @ B2))))). % insertI1
thf(fact_147_insertI1, axiom,
    ((![A2 : hoare_958474565_state, B2 : set_Ho840737317_state]: (member109514606_state @ A2 @ (insert776267541_state @ A2 @ B2))))). % insertI1
thf(fact_148_insertE, axiom,
    ((![A2 : pname, B3 : pname, A : set_pname]: ((member_pname @ A2 @ (insert_pname @ B3 @ A)) => ((~ ((A2 = B3))) => (member_pname @ A2 @ A)))))). % insertE
thf(fact_149_insertE, axiom,
    ((![A2 : hoare_958474565_state, B3 : hoare_958474565_state, A : set_Ho840737317_state]: ((member109514606_state @ A2 @ (insert776267541_state @ B3 @ A)) => ((~ ((A2 = B3))) => (member109514606_state @ A2 @ A)))))). % insertE
thf(fact_150_Compr__image__eq, axiom,
    ((![F : pname > hoare_958474565_state, A : set_pname, P : hoare_958474565_state > $o]: ((collec305460656_state @ (^[X2 : hoare_958474565_state]: (((member109514606_state @ X2 @ (image_2144627828_state @ F @ A))) & ((P @ X2))))) = (image_2144627828_state @ F @ (collect_pname @ (^[X2 : pname]: (((member_pname @ X2 @ A)) & ((P @ (F @ X2))))))))))). % Compr_image_eq
thf(fact_151_Compr__image__eq, axiom,
    ((![F : hoare_958474565_state > hoare_958474565_state, A : set_Ho840737317_state, P : hoare_958474565_state > $o]: ((collec305460656_state @ (^[X2 : hoare_958474565_state]: (((member109514606_state @ X2 @ (image_1849792670_state @ F @ A))) & ((P @ X2))))) = (image_1849792670_state @ F @ (collec305460656_state @ (^[X2 : hoare_958474565_state]: (((member109514606_state @ X2 @ A)) & ((P @ (F @ X2))))))))))). % Compr_image_eq
thf(fact_152_Compr__image__eq, axiom,
    ((![F : set_Ho840737317_state > hoare_958474565_state, A : set_se421025541_state, P : hoare_958474565_state > $o]: ((collec305460656_state @ (^[X2 : hoare_958474565_state]: (((member109514606_state @ X2 @ (image_1207908734_state @ F @ A))) & ((P @ X2))))) = (image_1207908734_state @ F @ (collec305218192_state @ (^[X2 : set_Ho840737317_state]: (((member1959617614_state @ X2 @ A)) & ((P @ (F @ X2))))))))))). % Compr_image_eq
thf(fact_153_Compr__image__eq, axiom,
    ((![F : set_pname > hoare_958474565_state, A : set_set_pname, P : hoare_958474565_state > $o]: ((collec305460656_state @ (^[X2 : hoare_958474565_state]: (((member109514606_state @ X2 @ (image_800262846_state @ F @ A))) & ((P @ X2))))) = (image_800262846_state @ F @ (collect_set_pname @ (^[X2 : set_pname]: (((member_set_pname @ X2 @ A)) & ((P @ (F @ X2))))))))))). % Compr_image_eq
thf(fact_154_Compr__image__eq, axiom,
    ((![F : hoare_958474565_state > set_Ho840737317_state, A : set_Ho840737317_state, P : set_Ho840737317_state > $o]: ((collec305218192_state @ (^[X2 : set_Ho840737317_state]: (((member1959617614_state @ X2 @ (image_1038902228_state @ F @ A))) & ((P @ X2))))) = (image_1038902228_state @ F @ (collec305460656_state @ (^[X2 : hoare_958474565_state]: (((member109514606_state @ X2 @ A)) & ((P @ (F @ X2))))))))))). % Compr_image_eq
thf(fact_155_Compr__image__eq, axiom,
    ((![F : set_Ho840737317_state > set_Ho840737317_state, A : set_se421025541_state, P : set_Ho840737317_state > $o]: ((collec305218192_state @ (^[X2 : set_Ho840737317_state]: (((member1959617614_state @ X2 @ (image_565609652_state @ F @ A))) & ((P @ X2))))) = (image_565609652_state @ F @ (collec305218192_state @ (^[X2 : set_Ho840737317_state]: (((member1959617614_state @ X2 @ A)) & ((P @ (F @ X2))))))))))). % Compr_image_eq
thf(fact_156_Compr__image__eq, axiom,
    ((![F : set_pname > set_Ho840737317_state, A : set_set_pname, P : set_Ho840737317_state > $o]: ((collec305218192_state @ (^[X2 : set_Ho840737317_state]: (((member1959617614_state @ X2 @ (image_434380702_state @ F @ A))) & ((P @ X2))))) = (image_434380702_state @ F @ (collect_set_pname @ (^[X2 : set_pname]: (((member_set_pname @ X2 @ A)) & ((P @ (F @ X2))))))))))). % Compr_image_eq
thf(fact_157_Compr__image__eq, axiom,
    ((![F : hoare_958474565_state > set_pname, A : set_Ho840737317_state, P : set_pname > $o]: ((collect_set_pname @ (^[X2 : set_pname]: (((member_set_pname @ X2 @ (image_222083648_pname @ F @ A))) & ((P @ X2))))) = (image_222083648_pname @ F @ (collec305460656_state @ (^[X2 : hoare_958474565_state]: (((member109514606_state @ X2 @ A)) & ((P @ (F @ X2))))))))))). % Compr_image_eq
thf(fact_158_Compr__image__eq, axiom,
    ((![F : set_Ho840737317_state > set_pname, A : set_se421025541_state, P : set_pname > $o]: ((collect_set_pname @ (^[X2 : set_pname]: (((member_set_pname @ X2 @ (image_2095143712_pname @ F @ A))) & ((P @ X2))))) = (image_2095143712_pname @ F @ (collec305218192_state @ (^[X2 : set_Ho840737317_state]: (((member1959617614_state @ X2 @ A)) & ((P @ (F @ X2))))))))))). % Compr_image_eq
thf(fact_159_Compr__image__eq, axiom,
    ((![F : set_pname > set_pname, A : set_set_pname, P : set_pname > $o]: ((collect_set_pname @ (^[X2 : set_pname]: (((member_set_pname @ X2 @ (image_1068293127_pname @ F @ A))) & ((P @ X2))))) = (image_1068293127_pname @ F @ (collect_set_pname @ (^[X2 : set_pname]: (((member_set_pname @ X2 @ A)) & ((P @ (F @ X2))))))))))). % Compr_image_eq
thf(fact_160_image__image, axiom,
    ((![F : pname > hoare_958474565_state, G3 : pname > pname, A : set_pname]: ((image_2144627828_state @ F @ (image_pname_pname @ G3 @ A)) = (image_2144627828_state @ (^[X2 : pname]: (F @ (G3 @ X2))) @ A))))). % image_image
thf(fact_161_image__image, axiom,
    ((![F : pname > hoare_958474565_state, G3 : hoare_958474565_state > pname, A : set_Ho840737317_state]: ((image_2144627828_state @ F @ (image_871391498_pname @ G3 @ A)) = (image_1849792670_state @ (^[X2 : hoare_958474565_state]: (F @ (G3 @ X2))) @ A))))). % image_image
thf(fact_162_image__image, axiom,
    ((![F : hoare_958474565_state > hoare_958474565_state, G3 : pname > hoare_958474565_state, A : set_pname]: ((image_1849792670_state @ F @ (image_2144627828_state @ G3 @ A)) = (image_2144627828_state @ (^[X2 : pname]: (F @ (G3 @ X2))) @ A))))). % image_image
thf(fact_163_image__image, axiom,
    ((![F : hoare_958474565_state > hoare_958474565_state, G3 : hoare_958474565_state > hoare_958474565_state, A : set_Ho840737317_state]: ((image_1849792670_state @ F @ (image_1849792670_state @ G3 @ A)) = (image_1849792670_state @ (^[X2 : hoare_958474565_state]: (F @ (G3 @ X2))) @ A))))). % image_image
thf(fact_164_imageE, axiom,
    ((![B3 : hoare_958474565_state, F : pname > hoare_958474565_state, A : set_pname]: ((member109514606_state @ B3 @ (image_2144627828_state @ F @ A)) => (~ ((![X3 : pname]: ((B3 = (F @ X3)) => (~ ((member_pname @ X3 @ A))))))))))). % imageE
thf(fact_165_imageE, axiom,
    ((![B3 : hoare_958474565_state, F : hoare_958474565_state > hoare_958474565_state, A : set_Ho840737317_state]: ((member109514606_state @ B3 @ (image_1849792670_state @ F @ A)) => (~ ((![X3 : hoare_958474565_state]: ((B3 = (F @ X3)) => (~ ((member109514606_state @ X3 @ A))))))))))). % imageE
thf(fact_166_pigeonhole__infinite__rel, axiom,
    ((![A : set_pname, B2 : set_pname, R : pname > pname > $o]: ((~ ((finite_finite_pname @ A))) => ((finite_finite_pname @ B2) => ((![X3 : pname]: ((member_pname @ X3 @ A) => (?[Xa : pname]: ((member_pname @ Xa @ B2) & (R @ X3 @ Xa))))) => (?[X3 : pname]: ((member_pname @ X3 @ B2) & (~ ((finite_finite_pname @ (collect_pname @ (^[A4 : pname]: (((member_pname @ A4 @ A)) & ((R @ A4 @ X3)))))))))))))))). % pigeonhole_infinite_rel
thf(fact_167_pigeonhole__infinite__rel, axiom,
    ((![A : set_Ho840737317_state, B2 : set_pname, R : hoare_958474565_state > pname > $o]: ((~ ((finite1986656878_state @ A))) => ((finite_finite_pname @ B2) => ((![X3 : hoare_958474565_state]: ((member109514606_state @ X3 @ A) => (?[Xa : pname]: ((member_pname @ Xa @ B2) & (R @ X3 @ Xa))))) => (?[X3 : pname]: ((member_pname @ X3 @ B2) & (~ ((finite1986656878_state @ (collec305460656_state @ (^[A4 : hoare_958474565_state]: (((member109514606_state @ A4 @ A)) & ((R @ A4 @ X3)))))))))))))))). % pigeonhole_infinite_rel
thf(fact_168_pigeonhole__infinite__rel, axiom,
    ((![A : set_pname, B2 : set_Ho840737317_state, R : pname > hoare_958474565_state > $o]: ((~ ((finite_finite_pname @ A))) => ((finite1986656878_state @ B2) => ((![X3 : pname]: ((member_pname @ X3 @ A) => (?[Xa : hoare_958474565_state]: ((member109514606_state @ Xa @ B2) & (R @ X3 @ Xa))))) => (?[X3 : hoare_958474565_state]: ((member109514606_state @ X3 @ B2) & (~ ((finite_finite_pname @ (collect_pname @ (^[A4 : pname]: (((member_pname @ A4 @ A)) & ((R @ A4 @ X3)))))))))))))))). % pigeonhole_infinite_rel
thf(fact_169_pigeonhole__infinite__rel, axiom,
    ((![A : set_pname, B2 : set_set_pname, R : pname > set_pname > $o]: ((~ ((finite_finite_pname @ A))) => ((finite505202775_pname @ B2) => ((![X3 : pname]: ((member_pname @ X3 @ A) => (?[Xa : set_pname]: ((member_set_pname @ Xa @ B2) & (R @ X3 @ Xa))))) => (?[X3 : set_pname]: ((member_set_pname @ X3 @ B2) & (~ ((finite_finite_pname @ (collect_pname @ (^[A4 : pname]: (((member_pname @ A4 @ A)) & ((R @ A4 @ X3)))))))))))))))). % pigeonhole_infinite_rel
thf(fact_170_pigeonhole__infinite__rel, axiom,
    ((![A : set_set_pname, B2 : set_pname, R : set_pname > pname > $o]: ((~ ((finite505202775_pname @ A))) => ((finite_finite_pname @ B2) => ((![X3 : set_pname]: ((member_set_pname @ X3 @ A) => (?[Xa : pname]: ((member_pname @ Xa @ B2) & (R @ X3 @ Xa))))) => (?[X3 : pname]: ((member_pname @ X3 @ B2) & (~ ((finite505202775_pname @ (collect_set_pname @ (^[A4 : set_pname]: (((member_set_pname @ A4 @ A)) & ((R @ A4 @ X3)))))))))))))))). % pigeonhole_infinite_rel
thf(fact_171_pigeonhole__infinite__rel, axiom,
    ((![A : set_Ho840737317_state, B2 : set_Ho840737317_state, R : hoare_958474565_state > hoare_958474565_state > $o]: ((~ ((finite1986656878_state @ A))) => ((finite1986656878_state @ B2) => ((![X3 : hoare_958474565_state]: ((member109514606_state @ X3 @ A) => (?[Xa : hoare_958474565_state]: ((member109514606_state @ Xa @ B2) & (R @ X3 @ Xa))))) => (?[X3 : hoare_958474565_state]: ((member109514606_state @ X3 @ B2) & (~ ((finite1986656878_state @ (collec305460656_state @ (^[A4 : hoare_958474565_state]: (((member109514606_state @ A4 @ A)) & ((R @ A4 @ X3)))))))))))))))). % pigeonhole_infinite_rel
thf(fact_172_pigeonhole__infinite__rel, axiom,
    ((![A : set_Ho840737317_state, B2 : set_set_pname, R : hoare_958474565_state > set_pname > $o]: ((~ ((finite1986656878_state @ A))) => ((finite505202775_pname @ B2) => ((![X3 : hoare_958474565_state]: ((member109514606_state @ X3 @ A) => (?[Xa : set_pname]: ((member_set_pname @ Xa @ B2) & (R @ X3 @ Xa))))) => (?[X3 : set_pname]: ((member_set_pname @ X3 @ B2) & (~ ((finite1986656878_state @ (collec305460656_state @ (^[A4 : hoare_958474565_state]: (((member109514606_state @ A4 @ A)) & ((R @ A4 @ X3)))))))))))))))). % pigeonhole_infinite_rel
thf(fact_173_pigeonhole__infinite__rel, axiom,
    ((![A : set_pname, B2 : set_se421025541_state, R : pname > set_Ho840737317_state > $o]: ((~ ((finite_finite_pname @ A))) => ((finite1266962254_state @ B2) => ((![X3 : pname]: ((member_pname @ X3 @ A) => (?[Xa : set_Ho840737317_state]: ((member1959617614_state @ Xa @ B2) & (R @ X3 @ Xa))))) => (?[X3 : set_Ho840737317_state]: ((member1959617614_state @ X3 @ B2) & (~ ((finite_finite_pname @ (collect_pname @ (^[A4 : pname]: (((member_pname @ A4 @ A)) & ((R @ A4 @ X3)))))))))))))))). % pigeonhole_infinite_rel
thf(fact_174_pigeonhole__infinite__rel, axiom,
    ((![A : set_se421025541_state, B2 : set_pname, R : set_Ho840737317_state > pname > $o]: ((~ ((finite1266962254_state @ A))) => ((finite_finite_pname @ B2) => ((![X3 : set_Ho840737317_state]: ((member1959617614_state @ X3 @ A) => (?[Xa : pname]: ((member_pname @ Xa @ B2) & (R @ X3 @ Xa))))) => (?[X3 : pname]: ((member_pname @ X3 @ B2) & (~ ((finite1266962254_state @ (collec305218192_state @ (^[A4 : set_Ho840737317_state]: (((member1959617614_state @ A4 @ A)) & ((R @ A4 @ X3)))))))))))))))). % pigeonhole_infinite_rel
thf(fact_175_pigeonhole__infinite__rel, axiom,
    ((![A : set_set_pname, B2 : set_Ho840737317_state, R : set_pname > hoare_958474565_state > $o]: ((~ ((finite505202775_pname @ A))) => ((finite1986656878_state @ B2) => ((![X3 : set_pname]: ((member_set_pname @ X3 @ A) => (?[Xa : hoare_958474565_state]: ((member109514606_state @ Xa @ B2) & (R @ X3 @ Xa))))) => (?[X3 : hoare_958474565_state]: ((member109514606_state @ X3 @ B2) & (~ ((finite505202775_pname @ (collect_set_pname @ (^[A4 : set_pname]: (((member_set_pname @ A4 @ A)) & ((R @ A4 @ X3)))))))))))))))). % pigeonhole_infinite_rel
thf(fact_176_not__finite__existsD, axiom,
    ((![P : hoare_958474565_state > $o]: ((~ ((finite1986656878_state @ (collec305460656_state @ P)))) => (?[X_1 : hoare_958474565_state]: (P @ X_1)))))). % not_finite_existsD
thf(fact_177_not__finite__existsD, axiom,
    ((![P : pname > $o]: ((~ ((finite_finite_pname @ (collect_pname @ P)))) => (?[X_1 : pname]: (P @ X_1)))))). % not_finite_existsD
thf(fact_178_not__finite__existsD, axiom,
    ((![P : set_Ho840737317_state > $o]: ((~ ((finite1266962254_state @ (collec305218192_state @ P)))) => (?[X_1 : set_Ho840737317_state]: (P @ X_1)))))). % not_finite_existsD
thf(fact_179_not__finite__existsD, axiom,
    ((![P : set_pname > $o]: ((~ ((finite505202775_pname @ (collect_set_pname @ P)))) => (?[X_1 : set_pname]: (P @ X_1)))))). % not_finite_existsD
thf(fact_180_Collect__subset, axiom,
    ((![A : set_se421025541_state, P : set_Ho840737317_state > $o]: (ord_le1363676837_state @ (collec305218192_state @ (^[X2 : set_Ho840737317_state]: (((member1959617614_state @ X2 @ A)) & ((P @ X2))))) @ A)))). % Collect_subset
thf(fact_181_Collect__subset, axiom,
    ((![A : set_set_pname, P : set_pname > $o]: (ord_le2066558166_pname @ (collect_set_pname @ (^[X2 : set_pname]: (((member_set_pname @ X2 @ A)) & ((P @ X2))))) @ A)))). % Collect_subset
thf(fact_182_Collect__subset, axiom,
    ((![A : set_Ho840737317_state, P : hoare_958474565_state > $o]: (ord_le1945819589_state @ (collec305460656_state @ (^[X2 : hoare_958474565_state]: (((member109514606_state @ X2 @ A)) & ((P @ X2))))) @ A)))). % Collect_subset
thf(fact_183_Collect__subset, axiom,
    ((![A : set_pname, P : pname > $o]: (ord_le865024672_pname @ (collect_pname @ (^[X2 : pname]: (((member_pname @ X2 @ A)) & ((P @ X2))))) @ A)))). % Collect_subset
thf(fact_184_insert__Collect, axiom,
    ((![A2 : hoare_958474565_state, P : hoare_958474565_state > $o]: ((insert776267541_state @ A2 @ (collec305460656_state @ P)) = (collec305460656_state @ (^[U : hoare_958474565_state]: (((~ ((U = A2)))) => ((P @ U))))))))). % insert_Collect
thf(fact_185_insert__Collect, axiom,
    ((![A2 : pname, P : pname > $o]: ((insert_pname @ A2 @ (collect_pname @ P)) = (collect_pname @ (^[U : pname]: (((~ ((U = A2)))) => ((P @ U))))))))). % insert_Collect
thf(fact_186_insert__Collect, axiom,
    ((![A2 : set_Ho840737317_state, P : set_Ho840737317_state > $o]: ((insert1860247541_state @ A2 @ (collec305218192_state @ P)) = (collec305218192_state @ (^[U : set_Ho840737317_state]: (((~ ((U = A2)))) => ((P @ U))))))))). % insert_Collect
thf(fact_187_insert__Collect, axiom,
    ((![A2 : set_pname, P : set_pname > $o]: ((insert_set_pname @ A2 @ (collect_set_pname @ P)) = (collect_set_pname @ (^[U : set_pname]: (((~ ((U = A2)))) => ((P @ U))))))))). % insert_Collect
thf(fact_188_insert__compr, axiom,
    ((insert_pname = (^[A4 : pname]: (^[B : set_pname]: (collect_pname @ (^[X2 : pname]: (((X2 = A4)) | ((member_pname @ X2 @ B)))))))))). % insert_compr
thf(fact_189_insert__compr, axiom,
    ((insert776267541_state = (^[A4 : hoare_958474565_state]: (^[B : set_Ho840737317_state]: (collec305460656_state @ (^[X2 : hoare_958474565_state]: (((X2 = A4)) | ((member109514606_state @ X2 @ B)))))))))). % insert_compr
thf(fact_190_insert__compr, axiom,
    ((insert1860247541_state = (^[A4 : set_Ho840737317_state]: (^[B : set_se421025541_state]: (collec305218192_state @ (^[X2 : set_Ho840737317_state]: (((X2 = A4)) | ((member1959617614_state @ X2 @ B)))))))))). % insert_compr
thf(fact_191_insert__compr, axiom,
    ((insert_set_pname = (^[A4 : set_pname]: (^[B : set_set_pname]: (collect_set_pname @ (^[X2 : set_pname]: (((X2 = A4)) | ((member_set_pname @ X2 @ B)))))))))). % insert_compr
thf(fact_192_finite__has__minimal2, axiom,
    ((![A : set_se421025541_state, A2 : set_Ho840737317_state]: ((finite1266962254_state @ A) => ((member1959617614_state @ A2 @ A) => (?[X3 : set_Ho840737317_state]: ((member1959617614_state @ X3 @ A) & ((ord_le1945819589_state @ X3 @ A2) & (![Xa : set_Ho840737317_state]: ((member1959617614_state @ Xa @ A) => ((ord_le1945819589_state @ Xa @ X3) => (X3 = Xa)))))))))))). % finite_has_minimal2
thf(fact_193_finite__has__minimal2, axiom,
    ((![A : set_set_pname, A2 : set_pname]: ((finite505202775_pname @ A) => ((member_set_pname @ A2 @ A) => (?[X3 : set_pname]: ((member_set_pname @ X3 @ A) & ((ord_le865024672_pname @ X3 @ A2) & (![Xa : set_pname]: ((member_set_pname @ Xa @ A) => ((ord_le865024672_pname @ Xa @ X3) => (X3 = Xa)))))))))))). % finite_has_minimal2
thf(fact_194_finite__has__maximal2, axiom,
    ((![A : set_se421025541_state, A2 : set_Ho840737317_state]: ((finite1266962254_state @ A) => ((member1959617614_state @ A2 @ A) => (?[X3 : set_Ho840737317_state]: ((member1959617614_state @ X3 @ A) & ((ord_le1945819589_state @ A2 @ X3) & (![Xa : set_Ho840737317_state]: ((member1959617614_state @ Xa @ A) => ((ord_le1945819589_state @ X3 @ Xa) => (X3 = Xa)))))))))))). % finite_has_maximal2
thf(fact_195_finite__has__maximal2, axiom,
    ((![A : set_set_pname, A2 : set_pname]: ((finite505202775_pname @ A) => ((member_set_pname @ A2 @ A) => (?[X3 : set_pname]: ((member_set_pname @ X3 @ A) & ((ord_le865024672_pname @ A2 @ X3) & (![Xa : set_pname]: ((member_set_pname @ Xa @ A) => ((ord_le865024672_pname @ X3 @ Xa) => (X3 = Xa)))))))))))). % finite_has_maximal2
thf(fact_196_all__subset__image, axiom,
    ((![F : hoare_958474565_state > hoare_958474565_state, A : set_Ho840737317_state, P : set_Ho840737317_state > $o]: ((![B : set_Ho840737317_state]: (((ord_le1945819589_state @ B @ (image_1849792670_state @ F @ A))) => ((P @ B)))) = (![B : set_Ho840737317_state]: (((ord_le1945819589_state @ B @ A)) => ((P @ (image_1849792670_state @ F @ B))))))))). % all_subset_image
thf(fact_197_all__subset__image, axiom,
    ((![F : pname > hoare_958474565_state, A : set_pname, P : set_Ho840737317_state > $o]: ((![B : set_Ho840737317_state]: (((ord_le1945819589_state @ B @ (image_2144627828_state @ F @ A))) => ((P @ B)))) = (![B : set_pname]: (((ord_le865024672_pname @ B @ A)) => ((P @ (image_2144627828_state @ F @ B))))))))). % all_subset_image
thf(fact_198_all__subset__image, axiom,
    ((![F : hoare_958474565_state > pname, A : set_Ho840737317_state, P : set_pname > $o]: ((![B : set_pname]: (((ord_le865024672_pname @ B @ (image_871391498_pname @ F @ A))) => ((P @ B)))) = (![B : set_Ho840737317_state]: (((ord_le1945819589_state @ B @ A)) => ((P @ (image_871391498_pname @ F @ B))))))))). % all_subset_image
thf(fact_199_all__subset__image, axiom,
    ((![F : pname > pname, A : set_pname, P : set_pname > $o]: ((![B : set_pname]: (((ord_le865024672_pname @ B @ (image_pname_pname @ F @ A))) => ((P @ B)))) = (![B : set_pname]: (((ord_le865024672_pname @ B @ A)) => ((P @ (image_pname_pname @ F @ B))))))))). % all_subset_image
thf(fact_200_subset__image__iff, axiom,
    ((![B2 : set_Ho840737317_state, F : hoare_958474565_state > hoare_958474565_state, A : set_Ho840737317_state]: ((ord_le1945819589_state @ B2 @ (image_1849792670_state @ F @ A)) = (?[AA : set_Ho840737317_state]: (((ord_le1945819589_state @ AA @ A)) & ((B2 = (image_1849792670_state @ F @ AA))))))))). % subset_image_iff
thf(fact_201_subset__image__iff, axiom,
    ((![B2 : set_Ho840737317_state, F : pname > hoare_958474565_state, A : set_pname]: ((ord_le1945819589_state @ B2 @ (image_2144627828_state @ F @ A)) = (?[AA : set_pname]: (((ord_le865024672_pname @ AA @ A)) & ((B2 = (image_2144627828_state @ F @ AA))))))))). % subset_image_iff
thf(fact_202_subset__image__iff, axiom,
    ((![B2 : set_pname, F : hoare_958474565_state > pname, A : set_Ho840737317_state]: ((ord_le865024672_pname @ B2 @ (image_871391498_pname @ F @ A)) = (?[AA : set_Ho840737317_state]: (((ord_le1945819589_state @ AA @ A)) & ((B2 = (image_871391498_pname @ F @ AA))))))))). % subset_image_iff
thf(fact_203_subset__image__iff, axiom,
    ((![B2 : set_pname, F : pname > pname, A : set_pname]: ((ord_le865024672_pname @ B2 @ (image_pname_pname @ F @ A)) = (?[AA : set_pname]: (((ord_le865024672_pname @ AA @ A)) & ((B2 = (image_pname_pname @ F @ AA))))))))). % subset_image_iff
thf(fact_204_image__subset__iff, axiom,
    ((![F : pname > hoare_958474565_state, A : set_pname, B2 : set_Ho840737317_state]: ((ord_le1945819589_state @ (image_2144627828_state @ F @ A) @ B2) = (![X2 : pname]: (((member_pname @ X2 @ A)) => ((member109514606_state @ (F @ X2) @ B2)))))))). % image_subset_iff
thf(fact_205_image__subset__iff, axiom,
    ((![F : hoare_958474565_state > hoare_958474565_state, A : set_Ho840737317_state, B2 : set_Ho840737317_state]: ((ord_le1945819589_state @ (image_1849792670_state @ F @ A) @ B2) = (![X2 : hoare_958474565_state]: (((member109514606_state @ X2 @ A)) => ((member109514606_state @ (F @ X2) @ B2)))))))). % image_subset_iff
thf(fact_206_subset__imageE, axiom,
    ((![B2 : set_Ho840737317_state, F : hoare_958474565_state > hoare_958474565_state, A : set_Ho840737317_state]: ((ord_le1945819589_state @ B2 @ (image_1849792670_state @ F @ A)) => (~ ((![C : set_Ho840737317_state]: ((ord_le1945819589_state @ C @ A) => (~ ((B2 = (image_1849792670_state @ F @ C)))))))))))). % subset_imageE
thf(fact_207_subset__imageE, axiom,
    ((![B2 : set_Ho840737317_state, F : pname > hoare_958474565_state, A : set_pname]: ((ord_le1945819589_state @ B2 @ (image_2144627828_state @ F @ A)) => (~ ((![C : set_pname]: ((ord_le865024672_pname @ C @ A) => (~ ((B2 = (image_2144627828_state @ F @ C)))))))))))). % subset_imageE
thf(fact_208_subset__imageE, axiom,
    ((![B2 : set_pname, F : hoare_958474565_state > pname, A : set_Ho840737317_state]: ((ord_le865024672_pname @ B2 @ (image_871391498_pname @ F @ A)) => (~ ((![C : set_Ho840737317_state]: ((ord_le1945819589_state @ C @ A) => (~ ((B2 = (image_871391498_pname @ F @ C)))))))))))). % subset_imageE
thf(fact_209_subset__imageE, axiom,
    ((![B2 : set_pname, F : pname > pname, A : set_pname]: ((ord_le865024672_pname @ B2 @ (image_pname_pname @ F @ A)) => (~ ((![C : set_pname]: ((ord_le865024672_pname @ C @ A) => (~ ((B2 = (image_pname_pname @ F @ C)))))))))))). % subset_imageE
thf(fact_210_image__subsetI, axiom,
    ((![A : set_pname, F : pname > hoare_958474565_state, B2 : set_Ho840737317_state]: ((![X3 : pname]: ((member_pname @ X3 @ A) => (member109514606_state @ (F @ X3) @ B2))) => (ord_le1945819589_state @ (image_2144627828_state @ F @ A) @ B2))))). % image_subsetI
thf(fact_211_image__subsetI, axiom,
    ((![A : set_Ho840737317_state, F : hoare_958474565_state > hoare_958474565_state, B2 : set_Ho840737317_state]: ((![X3 : hoare_958474565_state]: ((member109514606_state @ X3 @ A) => (member109514606_state @ (F @ X3) @ B2))) => (ord_le1945819589_state @ (image_1849792670_state @ F @ A) @ B2))))). % image_subsetI
thf(fact_212_image__subsetI, axiom,
    ((![A : set_Ho840737317_state, F : hoare_958474565_state > pname, B2 : set_pname]: ((![X3 : hoare_958474565_state]: ((member109514606_state @ X3 @ A) => (member_pname @ (F @ X3) @ B2))) => (ord_le865024672_pname @ (image_871391498_pname @ F @ A) @ B2))))). % image_subsetI
thf(fact_213_image__mono, axiom,
    ((![A : set_Ho840737317_state, B2 : set_Ho840737317_state, F : hoare_958474565_state > hoare_958474565_state]: ((ord_le1945819589_state @ A @ B2) => (ord_le1945819589_state @ (image_1849792670_state @ F @ A) @ (image_1849792670_state @ F @ B2)))))). % image_mono
thf(fact_214_image__mono, axiom,
    ((![A : set_Ho840737317_state, B2 : set_Ho840737317_state, F : hoare_958474565_state > pname]: ((ord_le1945819589_state @ A @ B2) => (ord_le865024672_pname @ (image_871391498_pname @ F @ A) @ (image_871391498_pname @ F @ B2)))))). % image_mono
thf(fact_215_image__mono, axiom,
    ((![A : set_pname, B2 : set_pname, F : pname > hoare_958474565_state]: ((ord_le865024672_pname @ A @ B2) => (ord_le1945819589_state @ (image_2144627828_state @ F @ A) @ (image_2144627828_state @ F @ B2)))))). % image_mono
thf(fact_216_image__mono, axiom,
    ((![A : set_pname, B2 : set_pname, F : pname > pname]: ((ord_le865024672_pname @ A @ B2) => (ord_le865024672_pname @ (image_pname_pname @ F @ A) @ (image_pname_pname @ F @ B2)))))). % image_mono
thf(fact_217_rev__finite__subset, axiom,
    ((![B2 : set_se421025541_state, A : set_se421025541_state]: ((finite1266962254_state @ B2) => ((ord_le1363676837_state @ A @ B2) => (finite1266962254_state @ A)))))). % rev_finite_subset
thf(fact_218_rev__finite__subset, axiom,
    ((![B2 : set_set_pname, A : set_set_pname]: ((finite505202775_pname @ B2) => ((ord_le2066558166_pname @ A @ B2) => (finite505202775_pname @ A)))))). % rev_finite_subset
thf(fact_219_rev__finite__subset, axiom,
    ((![B2 : set_Ho840737317_state, A : set_Ho840737317_state]: ((finite1986656878_state @ B2) => ((ord_le1945819589_state @ A @ B2) => (finite1986656878_state @ A)))))). % rev_finite_subset
thf(fact_220_rev__finite__subset, axiom,
    ((![B2 : set_pname, A : set_pname]: ((finite_finite_pname @ B2) => ((ord_le865024672_pname @ A @ B2) => (finite_finite_pname @ A)))))). % rev_finite_subset
thf(fact_221_infinite__super, axiom,
    ((![S3 : set_se421025541_state, T3 : set_se421025541_state]: ((ord_le1363676837_state @ S3 @ T3) => ((~ ((finite1266962254_state @ S3))) => (~ ((finite1266962254_state @ T3)))))))). % infinite_super
thf(fact_222_infinite__super, axiom,
    ((![S3 : set_set_pname, T3 : set_set_pname]: ((ord_le2066558166_pname @ S3 @ T3) => ((~ ((finite505202775_pname @ S3))) => (~ ((finite505202775_pname @ T3)))))))). % infinite_super
thf(fact_223_infinite__super, axiom,
    ((![S3 : set_Ho840737317_state, T3 : set_Ho840737317_state]: ((ord_le1945819589_state @ S3 @ T3) => ((~ ((finite1986656878_state @ S3))) => (~ ((finite1986656878_state @ T3)))))))). % infinite_super
thf(fact_224_infinite__super, axiom,
    ((![S3 : set_pname, T3 : set_pname]: ((ord_le865024672_pname @ S3 @ T3) => ((~ ((finite_finite_pname @ S3))) => (~ ((finite_finite_pname @ T3)))))))). % infinite_super
thf(fact_225_finite__subset, axiom,
    ((![A : set_se421025541_state, B2 : set_se421025541_state]: ((ord_le1363676837_state @ A @ B2) => ((finite1266962254_state @ B2) => (finite1266962254_state @ A)))))). % finite_subset
thf(fact_226_finite__subset, axiom,
    ((![A : set_set_pname, B2 : set_set_pname]: ((ord_le2066558166_pname @ A @ B2) => ((finite505202775_pname @ B2) => (finite505202775_pname @ A)))))). % finite_subset
thf(fact_227_finite__subset, axiom,
    ((![A : set_Ho840737317_state, B2 : set_Ho840737317_state]: ((ord_le1945819589_state @ A @ B2) => ((finite1986656878_state @ B2) => (finite1986656878_state @ A)))))). % finite_subset
thf(fact_228_finite__subset, axiom,
    ((![A : set_pname, B2 : set_pname]: ((ord_le865024672_pname @ A @ B2) => ((finite_finite_pname @ B2) => (finite_finite_pname @ A)))))). % finite_subset
thf(fact_229_finite_OinsertI, axiom,
    ((![A : set_Ho840737317_state, A2 : hoare_958474565_state]: ((finite1986656878_state @ A) => (finite1986656878_state @ (insert776267541_state @ A2 @ A)))))). % finite.insertI
thf(fact_230_finite_OinsertI, axiom,
    ((![A : set_pname, A2 : pname]: ((finite_finite_pname @ A) => (finite_finite_pname @ (insert_pname @ A2 @ A)))))). % finite.insertI
thf(fact_231_finite_OinsertI, axiom,
    ((![A : set_se421025541_state, A2 : set_Ho840737317_state]: ((finite1266962254_state @ A) => (finite1266962254_state @ (insert1860247541_state @ A2 @ A)))))). % finite.insertI
thf(fact_232_finite_OinsertI, axiom,
    ((![A : set_set_pname, A2 : set_pname]: ((finite505202775_pname @ A) => (finite505202775_pname @ (insert_set_pname @ A2 @ A)))))). % finite.insertI
thf(fact_233_subset__insertI2, axiom,
    ((![A : set_Ho840737317_state, B2 : set_Ho840737317_state, B3 : hoare_958474565_state]: ((ord_le1945819589_state @ A @ B2) => (ord_le1945819589_state @ A @ (insert776267541_state @ B3 @ B2)))))). % subset_insertI2
thf(fact_234_subset__insertI2, axiom,
    ((![A : set_pname, B2 : set_pname, B3 : pname]: ((ord_le865024672_pname @ A @ B2) => (ord_le865024672_pname @ A @ (insert_pname @ B3 @ B2)))))). % subset_insertI2
thf(fact_235_subset__insertI, axiom,
    ((![B2 : set_Ho840737317_state, A2 : hoare_958474565_state]: (ord_le1945819589_state @ B2 @ (insert776267541_state @ A2 @ B2))))). % subset_insertI
thf(fact_236_subset__insertI, axiom,
    ((![B2 : set_pname, A2 : pname]: (ord_le865024672_pname @ B2 @ (insert_pname @ A2 @ B2))))). % subset_insertI
thf(fact_237_subset__insert, axiom,
    ((![X : hoare_958474565_state, A : set_Ho840737317_state, B2 : set_Ho840737317_state]: ((~ ((member109514606_state @ X @ A))) => ((ord_le1945819589_state @ A @ (insert776267541_state @ X @ B2)) = (ord_le1945819589_state @ A @ B2)))))). % subset_insert
thf(fact_238_subset__insert, axiom,
    ((![X : pname, A : set_pname, B2 : set_pname]: ((~ ((member_pname @ X @ A))) => ((ord_le865024672_pname @ A @ (insert_pname @ X @ B2)) = (ord_le865024672_pname @ A @ B2)))))). % subset_insert
thf(fact_239_insert__mono, axiom,
    ((![C2 : set_Ho840737317_state, D : set_Ho840737317_state, A2 : hoare_958474565_state]: ((ord_le1945819589_state @ C2 @ D) => (ord_le1945819589_state @ (insert776267541_state @ A2 @ C2) @ (insert776267541_state @ A2 @ D)))))). % insert_mono
thf(fact_240_insert__mono, axiom,
    ((![C2 : set_pname, D : set_pname, A2 : pname]: ((ord_le865024672_pname @ C2 @ D) => (ord_le865024672_pname @ (insert_pname @ A2 @ C2) @ (insert_pname @ A2 @ D)))))). % insert_mono
thf(fact_241_pigeonhole__infinite, axiom,
    ((![A : set_set_pname, F : set_pname > set_Ho840737317_state]: ((~ ((finite505202775_pname @ A))) => ((finite1266962254_state @ (image_434380702_state @ F @ A)) => (?[X3 : set_pname]: ((member_set_pname @ X3 @ A) & (~ ((finite505202775_pname @ (collect_set_pname @ (^[A4 : set_pname]: (((member_set_pname @ A4 @ A)) & (((F @ A4) = (F @ X3)))))))))))))))). % pigeonhole_infinite
thf(fact_242_pigeonhole__infinite, axiom,
    ((![A : set_set_pname, F : set_pname > set_pname]: ((~ ((finite505202775_pname @ A))) => ((finite505202775_pname @ (image_1068293127_pname @ F @ A)) => (?[X3 : set_pname]: ((member_set_pname @ X3 @ A) & (~ ((finite505202775_pname @ (collect_set_pname @ (^[A4 : set_pname]: (((member_set_pname @ A4 @ A)) & (((F @ A4) = (F @ X3)))))))))))))))). % pigeonhole_infinite
thf(fact_243_finite__dom__body, axiom,
    ((finite_finite_pname @ (dom_pname_com @ body)))). % finite_dom_body
thf(fact_244_com_Oinject_I6_J, axiom,
    ((![X7 : pname, Y7 : pname]: (((body2 @ X7) = (body2 @ Y7)) = (X7 = Y7))))). % com.inject(6)
thf(fact_245_MGT__Body, axiom,
    ((![G2 : set_Ho840737317_state, Procs : set_pname]: ((hoare_604442164_state @ (sup_su737426425_state @ G2 @ (image_2144627828_state @ (^[Pn : pname]: (hoare_Mirabelle_MGT @ (body2 @ Pn))) @ Procs)) @ (image_2144627828_state @ (^[Pn : pname]: (hoare_Mirabelle_MGT @ (the_com @ (body @ Pn)))) @ Procs)) => ((finite_finite_pname @ Procs) => (hoare_604442164_state @ G2 @ (image_2144627828_state @ (^[Pn : pname]: (hoare_Mirabelle_MGT @ (body2 @ Pn))) @ Procs))))))). % MGT_Body
thf(fact_246_MGT__BodyN, axiom,
    ((![Pn2 : pname, G2 : set_Ho840737317_state]: ((hoare_604442164_state @ (insert776267541_state @ (hoare_Mirabelle_MGT @ (body2 @ Pn2)) @ G2) @ (insert776267541_state @ (hoare_Mirabelle_MGT @ (the_com @ (body @ Pn2))) @ bot_bo105666705_state)) => (hoare_604442164_state @ G2 @ (insert776267541_state @ (hoare_Mirabelle_MGT @ (body2 @ Pn2)) @ bot_bo105666705_state)))))). % MGT_BodyN
thf(fact_247_MGF__lemma1, axiom,
    ((![G2 : set_Ho840737317_state, C3 : com]: (hoare_405891322gleton => ((![X3 : pname]: ((member_pname @ X3 @ (dom_pname_com @ body)) => (hoare_604442164_state @ G2 @ (insert776267541_state @ (hoare_Mirabelle_MGT @ (body2 @ X3)) @ bot_bo105666705_state)))) => ((wt @ C3) => (hoare_604442164_state @ G2 @ (insert776267541_state @ (hoare_Mirabelle_MGT @ C3) @ bot_bo105666705_state)))))))). % MGF_lemma1

% Conjectures (6)
thf(conj_0, hypothesis,
    (hoare_405891322gleton)).
thf(conj_1, hypothesis,
    (wT_bodies)).
thf(conj_2, hypothesis,
    ((finite1986656878_state @ fa))).
thf(conj_3, hypothesis,
    ((~ ((member109514606_state @ x @ fa))))).
thf(conj_4, hypothesis,
    (((ord_le1945819589_state @ fa @ (image_2144627828_state @ (^[Pn : pname]: (hoare_Mirabelle_MGT @ (the_com @ (body @ Pn)))) @ (dom_pname_com @ body))) => (hoare_604442164_state @ (image_2144627828_state @ (^[Pn : pname]: (hoare_Mirabelle_MGT @ (body2 @ Pn))) @ (dom_pname_com @ body)) @ fa)))).
thf(conj_5, conjecture,
    (((~ ((ord_le1945819589_state @ (insert776267541_state @ x @ fa) @ (image_2144627828_state @ (^[Pn : pname]: (hoare_Mirabelle_MGT @ (the_com @ (body @ Pn)))) @ (dom_pname_com @ body))))) | (hoare_604442164_state @ (image_2144627828_state @ (^[Pn : pname]: (hoare_Mirabelle_MGT @ (body2 @ Pn))) @ (dom_pname_com @ body)) @ (insert776267541_state @ x @ fa))))).
