% 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_461__3254896_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:15:10.109

% Could-be-implicit typings (7)
thf(ty_n_t__Set__Oset_It__Hoare____Mirabelle____raqjowkjvm__Otriple_It__Com__Ostate_J_J, type,
    set_Ho840737317_state : $tType).
thf(ty_n_t__Hoare____Mirabelle____raqjowkjvm__Otriple_It__Com__Ostate_J, type,
    hoare_958474565_state : $tType).
thf(ty_n_t__Option__Ooption_It__Com__Ocom_J, type,
    option_com : $tType).
thf(ty_n_t__Set__Oset_It__Com__Opname_J, type,
    set_pname : $tType).
thf(ty_n_t__Com__Ostate, type,
    state : $tType).
thf(ty_n_t__Com__Opname, type,
    pname : $tType).
thf(ty_n_t__Com__Ocom, type,
    com : $tType).

% Explicit typings (35)
thf(sy_c_Com_OWT, type,
    wt : com > $o).
thf(sy_c_Com_OWT__bodies, type,
    wT_bodies : $o).
thf(sy_c_Com_Obody, type,
    body : pname > option_com).
thf(sy_c_Com_Ocom_OBODY, type,
    body2 : pname > com).
thf(sy_c_Hoare__Mirabelle__raqjowkjvm_OMGT, type,
    hoare_Mirabelle_MGT : com > hoare_958474565_state).
thf(sy_c_Hoare__Mirabelle__raqjowkjvm_Ohoare__derivs_001t__Com__Ostate, type,
    hoare_604442164_state : set_Ho840737317_state > set_Ho840737317_state > $o).
thf(sy_c_Hoare__Mirabelle__raqjowkjvm_Ostate__not__singleton, type,
    hoare_405891322gleton : $o).
thf(sy_c_Hoare__Mirabelle__raqjowkjvm_Otriple_Otriple_001t__Com__Ostate, type,
    hoare_1659279548_state : (state > state > $o) > com > (state > state > $o) > hoare_958474565_state).
thf(sy_c_Map_Odom_001t__Com__Opname_001t__Com__Ocom, type,
    dom_pname_com : (pname > option_com) > set_pname).
thf(sy_c_Map_Odom_001t__Hoare____Mirabelle____raqjowkjvm__Otriple_It__Com__Ostate_J_001t__Com__Ocom, type,
    dom_Ho256784515te_com : (hoare_958474565_state > option_com) > set_Ho840737317_state).
thf(sy_c_Option_Ooption_OSome_001t__Com__Ocom, type,
    some_com : com > option_com).
thf(sy_c_Option_Ooption_Othe_001t__Com__Ocom, type,
    the_com : option_com > com).
thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Hoare____Mirabelle____raqjowkjvm__Otriple_It__Com__Ostate_J_M_Eo_J, type,
    bot_bo1428770700tate_o : hoare_958474565_state > $o).
thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Com__Opname_J, type,
    bot_bot_set_pname : set_pname).
thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Hoare____Mirabelle____raqjowkjvm__Otriple_It__Com__Ostate_J_J, type,
    bot_bo105666705_state : set_Ho840737317_state).
thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Com__Opname_M_Eo_J, type,
    ord_less_eq_pname_o : (pname > $o) > (pname > $o) > $o).
thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Hoare____Mirabelle____raqjowkjvm__Otriple_It__Com__Ostate_J_M_Eo_J, type,
    ord_le1483368280tate_o : (hoare_958474565_state > $o) > (hoare_958474565_state > $o) > $o).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Com__Opname_J, type,
    ord_le865024672_pname : set_pname > set_pname > $o).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Hoare____Mirabelle____raqjowkjvm__Otriple_It__Com__Ostate_J_J, type,
    ord_le1945819589_state : set_Ho840737317_state > set_Ho840737317_state > $o).
thf(sy_c_Set_OCollect_001t__Com__Opname, type,
    collect_pname : (pname > $o) > set_pname).
thf(sy_c_Set_OCollect_001t__Hoare____Mirabelle____raqjowkjvm__Otriple_It__Com__Ostate_J, type,
    collec305460656_state : (hoare_958474565_state > $o) > set_Ho840737317_state).
thf(sy_c_Set_Oimage_001t__Com__Opname_001t__Com__Opname, type,
    image_pname_pname : (pname > pname) > set_pname > set_pname).
thf(sy_c_Set_Oimage_001t__Com__Opname_001t__Hoare____Mirabelle____raqjowkjvm__Otriple_It__Com__Ostate_J, type,
    image_2144627828_state : (pname > hoare_958474565_state) > set_pname > set_Ho840737317_state).
thf(sy_c_Set_Oimage_001t__Hoare____Mirabelle____raqjowkjvm__Otriple_It__Com__Ostate_J_001t__Com__Opname, type,
    image_871391498_pname : (hoare_958474565_state > pname) > set_Ho840737317_state > set_pname).
thf(sy_c_Set_Oimage_001t__Hoare____Mirabelle____raqjowkjvm__Otriple_It__Com__Ostate_J_001t__Hoare____Mirabelle____raqjowkjvm__Otriple_It__Com__Ostate_J, type,
    image_1849792670_state : (hoare_958474565_state > hoare_958474565_state) > set_Ho840737317_state > set_Ho840737317_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_Ois__singleton_001t__Com__Opname, type,
    is_singleton_pname : set_pname > $o).
thf(sy_c_Set_Ois__singleton_001t__Hoare____Mirabelle____raqjowkjvm__Otriple_It__Com__Ostate_J, type,
    is_sin536631353_state : set_Ho840737317_state > $o).
thf(sy_c_Set_Othe__elem_001t__Hoare____Mirabelle____raqjowkjvm__Otriple_It__Com__Ostate_J, type,
    the_el1300254266_state : set_Ho840737317_state > hoare_958474565_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_v_c, type,
    c : com).
thf(sy_v_pn, type,
    pn : pname).
thf(sy_v_y, type,
    y : com).

% Relevant facts (202)
thf(fact_0_single__stateE, axiom,
    ((hoare_405891322gleton => (![T : state]: (~ ((![S : state]: (S = T)))))))). % single_stateE
thf(fact_1_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_2_state__not__singleton__def, axiom,
    ((hoare_405891322gleton = (?[S2 : state]: (?[T2 : state]: (~ ((S2 = T2)))))))). % state_not_singleton_def
thf(fact_3_WT__bodiesD, axiom,
    ((![Pn : pname, B : com]: (wT_bodies => (((body @ Pn) = (some_com @ B)) => (wt @ B)))))). % WT_bodiesD
thf(fact_4_WTs__elim__cases_I7_J, axiom,
    ((![P : pname]: ((wt @ (body2 @ P)) => (~ ((![Y : com]: (~ (((body @ P) = (some_com @ Y))))))))))). % WTs_elim_cases(7)
thf(fact_5_MGF__lemma2__simult, axiom,
    ((![F : set_Ho840737317_state]: (hoare_405891322gleton => (wT_bodies => ((ord_le1945819589_state @ F @ (image_2144627828_state @ (^[Pn2 : pname]: (hoare_Mirabelle_MGT @ (the_com @ (body @ Pn2)))) @ (dom_pname_com @ body))) => (hoare_604442164_state @ (image_2144627828_state @ (^[Pn2 : pname]: (hoare_Mirabelle_MGT @ (body2 @ Pn2))) @ (dom_pname_com @ body)) @ F))))))). % MGF_lemma2_simult
thf(fact_6_com_Oinject_I6_J, axiom,
    ((![X7 : pname, Y7 : pname]: (((body2 @ X7) = (body2 @ Y7)) = (X7 = Y7))))). % com.inject(6)
thf(fact_7_option_Oinject, axiom,
    ((![X2 : com, Y2 : com]: (((some_com @ X2) = (some_com @ Y2)) = (X2 = Y2))))). % option.inject
thf(fact_8_image__eqI, axiom,
    ((![B : pname, F2 : pname > pname, X : pname, A : set_pname]: ((B = (F2 @ X)) => ((member_pname @ X @ A) => (member_pname @ B @ (image_pname_pname @ F2 @ A))))))). % image_eqI
thf(fact_9_image__eqI, axiom,
    ((![B : pname, F2 : hoare_958474565_state > pname, X : hoare_958474565_state, A : set_Ho840737317_state]: ((B = (F2 @ X)) => ((member109514606_state @ X @ A) => (member_pname @ B @ (image_871391498_pname @ F2 @ A))))))). % image_eqI
thf(fact_10_image__eqI, axiom,
    ((![B : hoare_958474565_state, F2 : hoare_958474565_state > hoare_958474565_state, X : hoare_958474565_state, A : set_Ho840737317_state]: ((B = (F2 @ X)) => ((member109514606_state @ X @ A) => (member109514606_state @ B @ (image_1849792670_state @ F2 @ A))))))). % image_eqI
thf(fact_11_image__eqI, axiom,
    ((![B : hoare_958474565_state, F2 : pname > hoare_958474565_state, X : pname, A : set_pname]: ((B = (F2 @ X)) => ((member_pname @ X @ A) => (member109514606_state @ B @ (image_2144627828_state @ F2 @ A))))))). % image_eqI
thf(fact_12_option_Osel, axiom,
    ((![X2 : com]: ((the_com @ (some_com @ X2)) = X2)))). % option.sel
thf(fact_13_domD, axiom,
    ((![A2 : pname, M : pname > option_com]: ((member_pname @ A2 @ (dom_pname_com @ M)) => (?[B2 : com]: ((M @ A2) = (some_com @ B2))))))). % domD
thf(fact_14_domD, axiom,
    ((![A2 : hoare_958474565_state, M : hoare_958474565_state > option_com]: ((member109514606_state @ A2 @ (dom_Ho256784515te_com @ M)) => (?[B2 : com]: ((M @ A2) = (some_com @ B2))))))). % domD
thf(fact_15_domI, axiom,
    ((![M : pname > option_com, A2 : pname, B : com]: (((M @ A2) = (some_com @ B)) => (member_pname @ A2 @ (dom_pname_com @ M)))))). % domI
thf(fact_16_domI, axiom,
    ((![M : hoare_958474565_state > option_com, A2 : hoare_958474565_state, B : com]: (((M @ A2) = (some_com @ B)) => (member109514606_state @ A2 @ (dom_Ho256784515te_com @ M)))))). % domI
thf(fact_17_MGF__lemma1, axiom,
    ((![G2 : set_Ho840737317_state, C : 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 @ C) => (hoare_604442164_state @ G2 @ (insert776267541_state @ (hoare_Mirabelle_MGT @ C) @ bot_bo105666705_state)))))))). % MGF_lemma1
thf(fact_18_imageE, axiom,
    ((![B : pname, F2 : pname > pname, A : set_pname]: ((member_pname @ B @ (image_pname_pname @ F2 @ A)) => (~ ((![X3 : pname]: ((B = (F2 @ X3)) => (~ ((member_pname @ X3 @ A))))))))))). % imageE
thf(fact_19_imageE, axiom,
    ((![B : pname, F2 : hoare_958474565_state > pname, A : set_Ho840737317_state]: ((member_pname @ B @ (image_871391498_pname @ F2 @ A)) => (~ ((![X3 : hoare_958474565_state]: ((B = (F2 @ X3)) => (~ ((member109514606_state @ X3 @ A))))))))))). % imageE
thf(fact_20_imageE, axiom,
    ((![B : hoare_958474565_state, F2 : pname > hoare_958474565_state, A : set_pname]: ((member109514606_state @ B @ (image_2144627828_state @ F2 @ A)) => (~ ((![X3 : pname]: ((B = (F2 @ X3)) => (~ ((member_pname @ X3 @ A))))))))))). % imageE
thf(fact_21_imageE, axiom,
    ((![B : hoare_958474565_state, F2 : hoare_958474565_state > hoare_958474565_state, A : set_Ho840737317_state]: ((member109514606_state @ B @ (image_1849792670_state @ F2 @ A)) => (~ ((![X3 : hoare_958474565_state]: ((B = (F2 @ X3)) => (~ ((member109514606_state @ X3 @ A))))))))))). % imageE
thf(fact_22_empty__iff, axiom,
    ((![C : pname]: (~ ((member_pname @ C @ bot_bot_set_pname)))))). % empty_iff
thf(fact_23_empty__iff, axiom,
    ((![C : hoare_958474565_state]: (~ ((member109514606_state @ C @ bot_bo105666705_state)))))). % empty_iff
thf(fact_24_all__not__in__conv, axiom,
    ((![A : set_pname]: ((![X4 : pname]: (~ ((member_pname @ X4 @ A)))) = (A = bot_bot_set_pname))))). % all_not_in_conv
thf(fact_25_all__not__in__conv, axiom,
    ((![A : set_Ho840737317_state]: ((![X4 : hoare_958474565_state]: (~ ((member109514606_state @ X4 @ A)))) = (A = bot_bo105666705_state))))). % all_not_in_conv
thf(fact_26_Collect__empty__eq, axiom,
    ((![P : hoare_958474565_state > $o]: (((collec305460656_state @ P) = bot_bo105666705_state) = (![X4 : hoare_958474565_state]: (~ ((P @ X4)))))))). % Collect_empty_eq
thf(fact_27_empty__Collect__eq, axiom,
    ((![P : hoare_958474565_state > $o]: ((bot_bo105666705_state = (collec305460656_state @ P)) = (![X4 : hoare_958474565_state]: (~ ((P @ X4)))))))). % empty_Collect_eq
thf(fact_28_subsetI, axiom,
    ((![A : set_pname, B3 : set_pname]: ((![X3 : pname]: ((member_pname @ X3 @ A) => (member_pname @ X3 @ B3))) => (ord_le865024672_pname @ A @ B3))))). % subsetI
thf(fact_29_subsetI, axiom,
    ((![A : set_Ho840737317_state, B3 : set_Ho840737317_state]: ((![X3 : hoare_958474565_state]: ((member109514606_state @ X3 @ A) => (member109514606_state @ X3 @ B3))) => (ord_le1945819589_state @ A @ B3))))). % subsetI
thf(fact_30_subset__antisym, axiom,
    ((![A : set_Ho840737317_state, B3 : set_Ho840737317_state]: ((ord_le1945819589_state @ A @ B3) => ((ord_le1945819589_state @ B3 @ A) => (A = B3)))))). % subset_antisym
thf(fact_31_insertCI, axiom,
    ((![A2 : pname, B3 : set_pname, B : pname]: (((~ ((member_pname @ A2 @ B3))) => (A2 = B)) => (member_pname @ A2 @ (insert_pname @ B @ B3)))))). % insertCI
thf(fact_32_insertCI, axiom,
    ((![A2 : hoare_958474565_state, B3 : set_Ho840737317_state, B : hoare_958474565_state]: (((~ ((member109514606_state @ A2 @ B3))) => (A2 = B)) => (member109514606_state @ A2 @ (insert776267541_state @ B @ B3)))))). % insertCI
thf(fact_33_insert__iff, axiom,
    ((![A2 : pname, B : pname, A : set_pname]: ((member_pname @ A2 @ (insert_pname @ B @ A)) = (((A2 = B)) | ((member_pname @ A2 @ A))))))). % insert_iff
thf(fact_34_insert__iff, axiom,
    ((![A2 : hoare_958474565_state, B : hoare_958474565_state, A : set_Ho840737317_state]: ((member109514606_state @ A2 @ (insert776267541_state @ B @ A)) = (((A2 = B)) | ((member109514606_state @ A2 @ A))))))). % insert_iff
thf(fact_35_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_36_image__is__empty, axiom,
    ((![F2 : pname > hoare_958474565_state, A : set_pname]: (((image_2144627828_state @ F2 @ A) = bot_bo105666705_state) = (A = bot_bot_set_pname))))). % image_is_empty
thf(fact_37_image__is__empty, axiom,
    ((![F2 : hoare_958474565_state > hoare_958474565_state, A : set_Ho840737317_state]: (((image_1849792670_state @ F2 @ A) = bot_bo105666705_state) = (A = bot_bo105666705_state))))). % image_is_empty
thf(fact_38_empty__is__image, axiom,
    ((![F2 : pname > hoare_958474565_state, A : set_pname]: ((bot_bo105666705_state = (image_2144627828_state @ F2 @ A)) = (A = bot_bot_set_pname))))). % empty_is_image
thf(fact_39_empty__is__image, axiom,
    ((![F2 : hoare_958474565_state > hoare_958474565_state, A : set_Ho840737317_state]: ((bot_bo105666705_state = (image_1849792670_state @ F2 @ A)) = (A = bot_bo105666705_state))))). % empty_is_image
thf(fact_40_image__empty, axiom,
    ((![F2 : pname > hoare_958474565_state]: ((image_2144627828_state @ F2 @ bot_bot_set_pname) = bot_bo105666705_state)))). % image_empty
thf(fact_41_image__empty, axiom,
    ((![F2 : hoare_958474565_state > hoare_958474565_state]: ((image_1849792670_state @ F2 @ bot_bo105666705_state) = bot_bo105666705_state)))). % image_empty
thf(fact_42_insert__image, axiom,
    ((![X : pname, A : set_pname, F2 : pname > hoare_958474565_state]: ((member_pname @ X @ A) => ((insert776267541_state @ (F2 @ X) @ (image_2144627828_state @ F2 @ A)) = (image_2144627828_state @ F2 @ A)))))). % insert_image
thf(fact_43_insert__image, axiom,
    ((![X : hoare_958474565_state, A : set_Ho840737317_state, F2 : hoare_958474565_state > hoare_958474565_state]: ((member109514606_state @ X @ A) => ((insert776267541_state @ (F2 @ X) @ (image_1849792670_state @ F2 @ A)) = (image_1849792670_state @ F2 @ A)))))). % insert_image
thf(fact_44_image__insert, axiom,
    ((![F2 : pname > hoare_958474565_state, A2 : pname, B3 : set_pname]: ((image_2144627828_state @ F2 @ (insert_pname @ A2 @ B3)) = (insert776267541_state @ (F2 @ A2) @ (image_2144627828_state @ F2 @ B3)))))). % image_insert
thf(fact_45_image__insert, axiom,
    ((![F2 : hoare_958474565_state > hoare_958474565_state, A2 : hoare_958474565_state, B3 : set_Ho840737317_state]: ((image_1849792670_state @ F2 @ (insert776267541_state @ A2 @ B3)) = (insert776267541_state @ (F2 @ A2) @ (image_1849792670_state @ F2 @ B3)))))). % image_insert
thf(fact_46_subset__empty, axiom,
    ((![A : set_Ho840737317_state]: ((ord_le1945819589_state @ A @ bot_bo105666705_state) = (A = bot_bo105666705_state))))). % subset_empty
thf(fact_47_empty__subsetI, axiom,
    ((![A : set_Ho840737317_state]: (ord_le1945819589_state @ bot_bo105666705_state @ A)))). % empty_subsetI
thf(fact_48_singletonI, axiom,
    ((![A2 : pname]: (member_pname @ A2 @ (insert_pname @ A2 @ bot_bot_set_pname))))). % singletonI
thf(fact_49_singletonI, axiom,
    ((![A2 : hoare_958474565_state]: (member109514606_state @ A2 @ (insert776267541_state @ A2 @ bot_bo105666705_state))))). % singletonI
thf(fact_50_insert__subset, axiom,
    ((![X : pname, A : set_pname, B3 : set_pname]: ((ord_le865024672_pname @ (insert_pname @ X @ A) @ B3) = (((member_pname @ X @ B3)) & ((ord_le865024672_pname @ A @ B3))))))). % insert_subset
thf(fact_51_insert__subset, axiom,
    ((![X : hoare_958474565_state, A : set_Ho840737317_state, B3 : set_Ho840737317_state]: ((ord_le1945819589_state @ (insert776267541_state @ X @ A) @ B3) = (((member109514606_state @ X @ B3)) & ((ord_le1945819589_state @ A @ B3))))))). % insert_subset
thf(fact_52_singleton__conv, axiom,
    ((![A2 : hoare_958474565_state]: ((collec305460656_state @ (^[X4 : hoare_958474565_state]: (X4 = A2))) = (insert776267541_state @ A2 @ bot_bo105666705_state))))). % singleton_conv
thf(fact_53_singleton__conv2, axiom,
    ((![A2 : hoare_958474565_state]: ((collec305460656_state @ ((^[Y3 : hoare_958474565_state]: (^[Z : hoare_958474565_state]: (Y3 = Z))) @ A2)) = (insert776267541_state @ A2 @ bot_bo105666705_state))))). % singleton_conv2
thf(fact_54_singleton__insert__inj__eq, axiom,
    ((![B : hoare_958474565_state, A2 : hoare_958474565_state, A : set_Ho840737317_state]: (((insert776267541_state @ B @ bot_bo105666705_state) = (insert776267541_state @ A2 @ A)) = (((A2 = B)) & ((ord_le1945819589_state @ A @ (insert776267541_state @ B @ bot_bo105666705_state)))))))). % singleton_insert_inj_eq
thf(fact_55_singleton__insert__inj__eq_H, axiom,
    ((![A2 : hoare_958474565_state, A : set_Ho840737317_state, B : hoare_958474565_state]: (((insert776267541_state @ A2 @ A) = (insert776267541_state @ B @ bot_bo105666705_state)) = (((A2 = B)) & ((ord_le1945819589_state @ A @ (insert776267541_state @ B @ bot_bo105666705_state)))))))). % singleton_insert_inj_eq'
thf(fact_56_emptyE, axiom,
    ((![A2 : pname]: (~ ((member_pname @ A2 @ bot_bot_set_pname)))))). % emptyE
thf(fact_57_emptyE, axiom,
    ((![A2 : hoare_958474565_state]: (~ ((member109514606_state @ A2 @ bot_bo105666705_state)))))). % emptyE
thf(fact_58_in__mono, axiom,
    ((![A : set_pname, B3 : set_pname, X : pname]: ((ord_le865024672_pname @ A @ B3) => ((member_pname @ X @ A) => (member_pname @ X @ B3)))))). % in_mono
thf(fact_59_in__mono, axiom,
    ((![A : set_Ho840737317_state, B3 : set_Ho840737317_state, X : hoare_958474565_state]: ((ord_le1945819589_state @ A @ B3) => ((member109514606_state @ X @ A) => (member109514606_state @ X @ B3)))))). % in_mono
thf(fact_60_insertE, axiom,
    ((![A2 : pname, B : pname, A : set_pname]: ((member_pname @ A2 @ (insert_pname @ B @ A)) => ((~ ((A2 = B))) => (member_pname @ A2 @ A)))))). % insertE
thf(fact_61_insertE, axiom,
    ((![A2 : hoare_958474565_state, B : hoare_958474565_state, A : set_Ho840737317_state]: ((member109514606_state @ A2 @ (insert776267541_state @ B @ A)) => ((~ ((A2 = B))) => (member109514606_state @ A2 @ A)))))). % insertE
thf(fact_62_subsetD, axiom,
    ((![A : set_pname, B3 : set_pname, C : pname]: ((ord_le865024672_pname @ A @ B3) => ((member_pname @ C @ A) => (member_pname @ C @ B3)))))). % subsetD
thf(fact_63_subsetD, axiom,
    ((![A : set_Ho840737317_state, B3 : set_Ho840737317_state, C : hoare_958474565_state]: ((ord_le1945819589_state @ A @ B3) => ((member109514606_state @ C @ A) => (member109514606_state @ C @ B3)))))). % subsetD
thf(fact_64_equals0D, axiom,
    ((![A : set_pname, A2 : pname]: ((A = bot_bot_set_pname) => (~ ((member_pname @ A2 @ A))))))). % equals0D
thf(fact_65_equals0D, axiom,
    ((![A : set_Ho840737317_state, A2 : hoare_958474565_state]: ((A = bot_bo105666705_state) => (~ ((member109514606_state @ A2 @ A))))))). % equals0D
thf(fact_66_equals0I, axiom,
    ((![A : set_pname]: ((![Y : pname]: (~ ((member_pname @ Y @ A)))) => (A = bot_bot_set_pname))))). % equals0I
thf(fact_67_equals0I, axiom,
    ((![A : set_Ho840737317_state]: ((![Y : hoare_958474565_state]: (~ ((member109514606_state @ Y @ A)))) => (A = bot_bo105666705_state))))). % equals0I
thf(fact_68_insertI1, axiom,
    ((![A2 : pname, B3 : set_pname]: (member_pname @ A2 @ (insert_pname @ A2 @ B3))))). % insertI1
thf(fact_69_insertI1, axiom,
    ((![A2 : hoare_958474565_state, B3 : set_Ho840737317_state]: (member109514606_state @ A2 @ (insert776267541_state @ A2 @ B3))))). % insertI1
thf(fact_70_insertI2, axiom,
    ((![A2 : pname, B3 : set_pname, B : pname]: ((member_pname @ A2 @ B3) => (member_pname @ A2 @ (insert_pname @ B @ B3)))))). % insertI2
thf(fact_71_insertI2, axiom,
    ((![A2 : hoare_958474565_state, B3 : set_Ho840737317_state, B : hoare_958474565_state]: ((member109514606_state @ A2 @ B3) => (member109514606_state @ A2 @ (insert776267541_state @ B @ B3)))))). % insertI2
thf(fact_72_mem__Collect__eq, axiom,
    ((![A2 : pname, P : pname > $o]: ((member_pname @ A2 @ (collect_pname @ P)) = (P @ A2))))). % mem_Collect_eq
thf(fact_73_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_74_Collect__mem__eq, axiom,
    ((![A : set_pname]: ((collect_pname @ (^[X4 : pname]: (member_pname @ X4 @ A))) = A)))). % Collect_mem_eq
thf(fact_75_Collect__mem__eq, axiom,
    ((![A : set_Ho840737317_state]: ((collec305460656_state @ (^[X4 : hoare_958474565_state]: (member109514606_state @ X4 @ A))) = A)))). % Collect_mem_eq
thf(fact_76_empty__def, axiom,
    ((bot_bo105666705_state = (collec305460656_state @ (^[X4 : hoare_958474565_state]: $false))))). % empty_def
thf(fact_77_equalityE, axiom,
    ((![A : set_Ho840737317_state, B3 : set_Ho840737317_state]: ((A = B3) => (~ (((ord_le1945819589_state @ A @ B3) => (~ ((ord_le1945819589_state @ B3 @ A)))))))))). % equalityE
thf(fact_78_subset__eq, axiom,
    ((ord_le865024672_pname = (^[A3 : set_pname]: (^[B4 : set_pname]: (![X4 : pname]: (((member_pname @ X4 @ A3)) => ((member_pname @ X4 @ B4))))))))). % subset_eq
thf(fact_79_subset__eq, axiom,
    ((ord_le1945819589_state = (^[A3 : set_Ho840737317_state]: (^[B4 : set_Ho840737317_state]: (![X4 : hoare_958474565_state]: (((member109514606_state @ X4 @ A3)) => ((member109514606_state @ X4 @ B4))))))))). % subset_eq
thf(fact_80_equalityD1, axiom,
    ((![A : set_Ho840737317_state, B3 : set_Ho840737317_state]: ((A = B3) => (ord_le1945819589_state @ A @ B3))))). % equalityD1
thf(fact_81_equalityD2, axiom,
    ((![A : set_Ho840737317_state, B3 : set_Ho840737317_state]: ((A = B3) => (ord_le1945819589_state @ B3 @ A))))). % equalityD2
thf(fact_82_ex__in__conv, axiom,
    ((![A : set_pname]: ((?[X4 : pname]: (member_pname @ X4 @ A)) = (~ ((A = bot_bot_set_pname))))))). % ex_in_conv
thf(fact_83_ex__in__conv, axiom,
    ((![A : set_Ho840737317_state]: ((?[X4 : hoare_958474565_state]: (member109514606_state @ X4 @ A)) = (~ ((A = bot_bo105666705_state))))))). % ex_in_conv
thf(fact_84_Set_Oset__insert, axiom,
    ((![X : pname, A : set_pname]: ((member_pname @ X @ A) => (~ ((![B5 : set_pname]: ((A = (insert_pname @ X @ B5)) => (member_pname @ X @ B5))))))))). % Set.set_insert
thf(fact_85_Set_Oset__insert, axiom,
    ((![X : hoare_958474565_state, A : set_Ho840737317_state]: ((member109514606_state @ X @ A) => (~ ((![B5 : set_Ho840737317_state]: ((A = (insert776267541_state @ X @ B5)) => (member109514606_state @ X @ B5))))))))). % Set.set_insert
thf(fact_86_singletonD, axiom,
    ((![B : pname, A2 : pname]: ((member_pname @ B @ (insert_pname @ A2 @ bot_bot_set_pname)) => (B = A2))))). % singletonD
thf(fact_87_singletonD, axiom,
    ((![B : hoare_958474565_state, A2 : hoare_958474565_state]: ((member109514606_state @ B @ (insert776267541_state @ A2 @ bot_bo105666705_state)) => (B = A2))))). % singletonD
thf(fact_88_subset__iff, axiom,
    ((ord_le865024672_pname = (^[A3 : set_pname]: (^[B4 : set_pname]: (![T2 : pname]: (((member_pname @ T2 @ A3)) => ((member_pname @ T2 @ B4))))))))). % subset_iff
thf(fact_89_subset__iff, axiom,
    ((ord_le1945819589_state = (^[A3 : set_Ho840737317_state]: (^[B4 : set_Ho840737317_state]: (![T2 : hoare_958474565_state]: (((member109514606_state @ T2 @ A3)) => ((member109514606_state @ T2 @ B4))))))))). % subset_iff
thf(fact_90_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_91_subset__refl, axiom,
    ((![A : set_Ho840737317_state]: (ord_le1945819589_state @ A @ A)))). % subset_refl
thf(fact_92_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_93_insert__compr, axiom,
    ((insert_pname = (^[A4 : pname]: (^[B4 : set_pname]: (collect_pname @ (^[X4 : pname]: (((X4 = A4)) | ((member_pname @ X4 @ B4)))))))))). % insert_compr
thf(fact_94_insert__compr, axiom,
    ((insert776267541_state = (^[A4 : hoare_958474565_state]: (^[B4 : set_Ho840737317_state]: (collec305460656_state @ (^[X4 : hoare_958474565_state]: (((X4 = A4)) | ((member109514606_state @ X4 @ B4)))))))))). % insert_compr
thf(fact_95_insert__ident, axiom,
    ((![X : pname, A : set_pname, B3 : set_pname]: ((~ ((member_pname @ X @ A))) => ((~ ((member_pname @ X @ B3))) => (((insert_pname @ X @ A) = (insert_pname @ X @ B3)) = (A = B3))))))). % insert_ident
thf(fact_96_insert__ident, axiom,
    ((![X : hoare_958474565_state, A : set_Ho840737317_state, B3 : set_Ho840737317_state]: ((~ ((member109514606_state @ X @ A))) => ((~ ((member109514606_state @ X @ B3))) => (((insert776267541_state @ X @ A) = (insert776267541_state @ X @ B3)) = (A = B3))))))). % insert_ident
thf(fact_97_subset__trans, axiom,
    ((![A : set_Ho840737317_state, B3 : set_Ho840737317_state, C2 : set_Ho840737317_state]: ((ord_le1945819589_state @ A @ B3) => ((ord_le1945819589_state @ B3 @ C2) => (ord_le1945819589_state @ A @ C2)))))). % subset_trans
thf(fact_98_insert__absorb, axiom,
    ((![A2 : pname, A : set_pname]: ((member_pname @ A2 @ A) => ((insert_pname @ A2 @ A) = A))))). % insert_absorb
thf(fact_99_insert__absorb, axiom,
    ((![A2 : hoare_958474565_state, A : set_Ho840737317_state]: ((member109514606_state @ A2 @ A) => ((insert776267541_state @ A2 @ A) = A))))). % insert_absorb
thf(fact_100_insert__eq__iff, axiom,
    ((![A2 : pname, A : set_pname, B : pname, B3 : set_pname]: ((~ ((member_pname @ A2 @ A))) => ((~ ((member_pname @ B @ B3))) => (((insert_pname @ A2 @ A) = (insert_pname @ B @ B3)) = (((((A2 = B)) => ((A = B3)))) & ((((~ ((A2 = B)))) => ((?[C3 : set_pname]: (((A = (insert_pname @ B @ C3))) & ((((~ ((member_pname @ B @ C3)))) & ((((B3 = (insert_pname @ A2 @ C3))) & ((~ ((member_pname @ A2 @ C3)))))))))))))))))))). % insert_eq_iff
thf(fact_101_insert__eq__iff, axiom,
    ((![A2 : hoare_958474565_state, A : set_Ho840737317_state, B : hoare_958474565_state, B3 : set_Ho840737317_state]: ((~ ((member109514606_state @ A2 @ A))) => ((~ ((member109514606_state @ B @ B3))) => (((insert776267541_state @ A2 @ A) = (insert776267541_state @ B @ B3)) = (((((A2 = B)) => ((A = B3)))) & ((((~ ((A2 = B)))) => ((?[C3 : set_Ho840737317_state]: (((A = (insert776267541_state @ B @ C3))) & ((((~ ((member109514606_state @ B @ C3)))) & ((((B3 = (insert776267541_state @ A2 @ C3))) & ((~ ((member109514606_state @ A2 @ C3)))))))))))))))))))). % insert_eq_iff
thf(fact_102_set__eq__subset, axiom,
    (((^[Y3 : set_Ho840737317_state]: (^[Z : set_Ho840737317_state]: (Y3 = Z))) = (^[A3 : set_Ho840737317_state]: (^[B4 : set_Ho840737317_state]: (((ord_le1945819589_state @ A3 @ B4)) & ((ord_le1945819589_state @ B4 @ A3)))))))). % set_eq_subset
thf(fact_103_singleton__iff, axiom,
    ((![B : pname, A2 : pname]: ((member_pname @ B @ (insert_pname @ A2 @ bot_bot_set_pname)) = (B = A2))))). % singleton_iff
thf(fact_104_singleton__iff, axiom,
    ((![B : hoare_958474565_state, A2 : hoare_958474565_state]: ((member109514606_state @ B @ (insert776267541_state @ A2 @ bot_bo105666705_state)) = (B = A2))))). % singleton_iff
thf(fact_105_subset__insert, axiom,
    ((![X : pname, A : set_pname, B3 : set_pname]: ((~ ((member_pname @ X @ A))) => ((ord_le865024672_pname @ A @ (insert_pname @ X @ B3)) = (ord_le865024672_pname @ A @ B3)))))). % subset_insert
thf(fact_106_subset__insert, axiom,
    ((![X : hoare_958474565_state, A : set_Ho840737317_state, B3 : set_Ho840737317_state]: ((~ ((member109514606_state @ X @ A))) => ((ord_le1945819589_state @ A @ (insert776267541_state @ X @ B3)) = (ord_le1945819589_state @ A @ B3)))))). % subset_insert
thf(fact_107_Collect__subset, axiom,
    ((![A : set_pname, P : pname > $o]: (ord_le865024672_pname @ (collect_pname @ (^[X4 : pname]: (((member_pname @ X4 @ A)) & ((P @ X4))))) @ A)))). % Collect_subset
thf(fact_108_Collect__subset, axiom,
    ((![A : set_Ho840737317_state, P : hoare_958474565_state > $o]: (ord_le1945819589_state @ (collec305460656_state @ (^[X4 : hoare_958474565_state]: (((member109514606_state @ X4 @ A)) & ((P @ X4))))) @ A)))). % Collect_subset
thf(fact_109_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_110_insert__commute, axiom,
    ((![X : hoare_958474565_state, Y4 : hoare_958474565_state, A : set_Ho840737317_state]: ((insert776267541_state @ X @ (insert776267541_state @ Y4 @ A)) = (insert776267541_state @ Y4 @ (insert776267541_state @ X @ A)))))). % insert_commute
thf(fact_111_subset__insertI, axiom,
    ((![B3 : set_Ho840737317_state, A2 : hoare_958474565_state]: (ord_le1945819589_state @ B3 @ (insert776267541_state @ A2 @ B3))))). % subset_insertI
thf(fact_112_Collect__conv__if, axiom,
    ((![P : hoare_958474565_state > $o, A2 : hoare_958474565_state]: (((P @ A2) => ((collec305460656_state @ (^[X4 : hoare_958474565_state]: (((X4 = A2)) & ((P @ X4))))) = (insert776267541_state @ A2 @ bot_bo105666705_state))) & ((~ ((P @ A2))) => ((collec305460656_state @ (^[X4 : hoare_958474565_state]: (((X4 = A2)) & ((P @ X4))))) = bot_bo105666705_state)))))). % Collect_conv_if
thf(fact_113_subset__insertI2, axiom,
    ((![A : set_Ho840737317_state, B3 : set_Ho840737317_state, B : hoare_958474565_state]: ((ord_le1945819589_state @ A @ B3) => (ord_le1945819589_state @ A @ (insert776267541_state @ B @ B3)))))). % subset_insertI2
thf(fact_114_Collect__conv__if2, axiom,
    ((![P : hoare_958474565_state > $o, A2 : hoare_958474565_state]: (((P @ A2) => ((collec305460656_state @ (^[X4 : hoare_958474565_state]: (((A2 = X4)) & ((P @ X4))))) = (insert776267541_state @ A2 @ bot_bo105666705_state))) & ((~ ((P @ A2))) => ((collec305460656_state @ (^[X4 : hoare_958474565_state]: (((A2 = X4)) & ((P @ X4))))) = bot_bo105666705_state)))))). % Collect_conv_if2
thf(fact_115_Collect__mono__iff, axiom,
    ((![P : hoare_958474565_state > $o, Q : hoare_958474565_state > $o]: ((ord_le1945819589_state @ (collec305460656_state @ P) @ (collec305460656_state @ Q)) = (![X4 : hoare_958474565_state]: (((P @ X4)) => ((Q @ X4)))))))). % Collect_mono_iff
thf(fact_116_doubleton__eq__iff, axiom,
    ((![A2 : hoare_958474565_state, B : hoare_958474565_state, C : hoare_958474565_state, D2 : hoare_958474565_state]: (((insert776267541_state @ A2 @ (insert776267541_state @ B @ bot_bo105666705_state)) = (insert776267541_state @ C @ (insert776267541_state @ D2 @ bot_bo105666705_state))) = (((((A2 = C)) & ((B = D2)))) | ((((A2 = D2)) & ((B = C))))))))). % doubleton_eq_iff
thf(fact_117_insert__not__empty, axiom,
    ((![A2 : hoare_958474565_state, A : set_Ho840737317_state]: (~ (((insert776267541_state @ A2 @ A) = bot_bo105666705_state)))))). % insert_not_empty
thf(fact_118_singleton__inject, axiom,
    ((![A2 : hoare_958474565_state, B : hoare_958474565_state]: (((insert776267541_state @ A2 @ bot_bo105666705_state) = (insert776267541_state @ B @ bot_bo105666705_state)) => (A2 = B))))). % singleton_inject
thf(fact_119_subset__singletonD, axiom,
    ((![A : set_Ho840737317_state, X : hoare_958474565_state]: ((ord_le1945819589_state @ A @ (insert776267541_state @ X @ bot_bo105666705_state)) => ((A = bot_bo105666705_state) | (A = (insert776267541_state @ X @ bot_bo105666705_state))))))). % subset_singletonD
thf(fact_120_mk__disjoint__insert, axiom,
    ((![A2 : pname, A : set_pname]: ((member_pname @ A2 @ A) => (?[B5 : set_pname]: ((A = (insert_pname @ A2 @ B5)) & (~ ((member_pname @ A2 @ B5))))))))). % mk_disjoint_insert
thf(fact_121_mk__disjoint__insert, axiom,
    ((![A2 : hoare_958474565_state, A : set_Ho840737317_state]: ((member109514606_state @ A2 @ A) => (?[B5 : set_Ho840737317_state]: ((A = (insert776267541_state @ A2 @ B5)) & (~ ((member109514606_state @ A2 @ B5))))))))). % mk_disjoint_insert
thf(fact_122_subset__singleton__iff, axiom,
    ((![X5 : set_Ho840737317_state, A2 : hoare_958474565_state]: ((ord_le1945819589_state @ X5 @ (insert776267541_state @ A2 @ bot_bo105666705_state)) = (((X5 = bot_bo105666705_state)) | ((X5 = (insert776267541_state @ A2 @ bot_bo105666705_state)))))))). % subset_singleton_iff
thf(fact_123_image__constant__conv, axiom,
    ((![A : set_pname, C : hoare_958474565_state]: (((A = bot_bot_set_pname) => ((image_2144627828_state @ (^[X4 : pname]: C) @ A) = bot_bo105666705_state)) & ((~ ((A = bot_bot_set_pname))) => ((image_2144627828_state @ (^[X4 : pname]: C) @ A) = (insert776267541_state @ C @ bot_bo105666705_state))))))). % image_constant_conv
thf(fact_124_image__constant__conv, axiom,
    ((![A : set_Ho840737317_state, C : hoare_958474565_state]: (((A = bot_bo105666705_state) => ((image_1849792670_state @ (^[X4 : hoare_958474565_state]: C) @ A) = bot_bo105666705_state)) & ((~ ((A = bot_bo105666705_state))) => ((image_1849792670_state @ (^[X4 : hoare_958474565_state]: C) @ A) = (insert776267541_state @ C @ bot_bo105666705_state))))))). % image_constant_conv
thf(fact_125_image__constant, axiom,
    ((![X : pname, A : set_pname, C : hoare_958474565_state]: ((member_pname @ X @ A) => ((image_2144627828_state @ (^[X4 : pname]: C) @ A) = (insert776267541_state @ C @ bot_bo105666705_state)))))). % image_constant
thf(fact_126_image__constant, axiom,
    ((![X : hoare_958474565_state, A : set_Ho840737317_state, C : hoare_958474565_state]: ((member109514606_state @ X @ A) => ((image_1849792670_state @ (^[X4 : hoare_958474565_state]: C) @ A) = (insert776267541_state @ C @ bot_bo105666705_state)))))). % image_constant
thf(fact_127_hoare__derivs_Oinsert, axiom,
    ((![G2 : set_Ho840737317_state, T3 : hoare_958474565_state, Ts : set_Ho840737317_state]: ((hoare_604442164_state @ G2 @ (insert776267541_state @ T3 @ bot_bo105666705_state)) => ((hoare_604442164_state @ G2 @ Ts) => (hoare_604442164_state @ G2 @ (insert776267541_state @ T3 @ Ts))))))). % hoare_derivs.insert
thf(fact_128_derivs__insertD, axiom,
    ((![G2 : set_Ho840737317_state, T3 : hoare_958474565_state, Ts : set_Ho840737317_state]: ((hoare_604442164_state @ G2 @ (insert776267541_state @ T3 @ Ts)) => ((hoare_604442164_state @ G2 @ (insert776267541_state @ T3 @ bot_bo105666705_state)) & (hoare_604442164_state @ G2 @ Ts)))))). % derivs_insertD
thf(fact_129_subset__image__iff, axiom,
    ((![B3 : set_Ho840737317_state, F2 : pname > hoare_958474565_state, A : set_pname]: ((ord_le1945819589_state @ B3 @ (image_2144627828_state @ F2 @ A)) = (?[AA : set_pname]: (((ord_le865024672_pname @ AA @ A)) & ((B3 = (image_2144627828_state @ F2 @ AA))))))))). % subset_image_iff
thf(fact_130_subset__image__iff, axiom,
    ((![B3 : set_Ho840737317_state, F2 : hoare_958474565_state > hoare_958474565_state, A : set_Ho840737317_state]: ((ord_le1945819589_state @ B3 @ (image_1849792670_state @ F2 @ A)) = (?[AA : set_Ho840737317_state]: (((ord_le1945819589_state @ AA @ A)) & ((B3 = (image_1849792670_state @ F2 @ AA))))))))). % subset_image_iff
thf(fact_131_image__subset__iff, axiom,
    ((![F2 : pname > hoare_958474565_state, A : set_pname, B3 : set_Ho840737317_state]: ((ord_le1945819589_state @ (image_2144627828_state @ F2 @ A) @ B3) = (![X4 : pname]: (((member_pname @ X4 @ A)) => ((member109514606_state @ (F2 @ X4) @ B3)))))))). % image_subset_iff
thf(fact_132_subset__imageE, axiom,
    ((![B3 : set_Ho840737317_state, F2 : pname > hoare_958474565_state, A : set_pname]: ((ord_le1945819589_state @ B3 @ (image_2144627828_state @ F2 @ A)) => (~ ((![C4 : set_pname]: ((ord_le865024672_pname @ C4 @ A) => (~ ((B3 = (image_2144627828_state @ F2 @ C4)))))))))))). % subset_imageE
thf(fact_133_subset__imageE, axiom,
    ((![B3 : set_Ho840737317_state, F2 : hoare_958474565_state > hoare_958474565_state, A : set_Ho840737317_state]: ((ord_le1945819589_state @ B3 @ (image_1849792670_state @ F2 @ A)) => (~ ((![C4 : set_Ho840737317_state]: ((ord_le1945819589_state @ C4 @ A) => (~ ((B3 = (image_1849792670_state @ F2 @ C4)))))))))))). % subset_imageE
thf(fact_134_image__subsetI, axiom,
    ((![A : set_pname, F2 : pname > pname, B3 : set_pname]: ((![X3 : pname]: ((member_pname @ X3 @ A) => (member_pname @ (F2 @ X3) @ B3))) => (ord_le865024672_pname @ (image_pname_pname @ F2 @ A) @ B3))))). % image_subsetI
thf(fact_135_image__subsetI, axiom,
    ((![A : set_Ho840737317_state, F2 : hoare_958474565_state > pname, B3 : set_pname]: ((![X3 : hoare_958474565_state]: ((member109514606_state @ X3 @ A) => (member_pname @ (F2 @ X3) @ B3))) => (ord_le865024672_pname @ (image_871391498_pname @ F2 @ A) @ B3))))). % image_subsetI
thf(fact_136_image__subsetI, axiom,
    ((![A : set_pname, F2 : pname > hoare_958474565_state, B3 : set_Ho840737317_state]: ((![X3 : pname]: ((member_pname @ X3 @ A) => (member109514606_state @ (F2 @ X3) @ B3))) => (ord_le1945819589_state @ (image_2144627828_state @ F2 @ A) @ B3))))). % image_subsetI
thf(fact_137_image__subsetI, axiom,
    ((![A : set_Ho840737317_state, F2 : hoare_958474565_state > hoare_958474565_state, B3 : set_Ho840737317_state]: ((![X3 : hoare_958474565_state]: ((member109514606_state @ X3 @ A) => (member109514606_state @ (F2 @ X3) @ B3))) => (ord_le1945819589_state @ (image_1849792670_state @ F2 @ A) @ B3))))). % image_subsetI
thf(fact_138_image__mono, axiom,
    ((![A : set_pname, B3 : set_pname, F2 : pname > hoare_958474565_state]: ((ord_le865024672_pname @ A @ B3) => (ord_le1945819589_state @ (image_2144627828_state @ F2 @ A) @ (image_2144627828_state @ F2 @ B3)))))). % image_mono
thf(fact_139_image__mono, axiom,
    ((![A : set_Ho840737317_state, B3 : set_Ho840737317_state, F2 : hoare_958474565_state > hoare_958474565_state]: ((ord_le1945819589_state @ A @ B3) => (ord_le1945819589_state @ (image_1849792670_state @ F2 @ A) @ (image_1849792670_state @ F2 @ B3)))))). % image_mono
thf(fact_140_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_141_asm, axiom,
    ((![Ts : set_Ho840737317_state, G2 : set_Ho840737317_state]: ((ord_le1945819589_state @ Ts @ G2) => (hoare_604442164_state @ G2 @ Ts))))). % asm
thf(fact_142_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_143_empty, axiom,
    ((![G2 : set_Ho840737317_state]: (hoare_604442164_state @ G2 @ bot_bo105666705_state)))). % empty
thf(fact_144_insert__dom, axiom,
    ((![F2 : pname > option_com, X : pname, Y4 : com]: (((F2 @ X) = (some_com @ Y4)) => ((insert_pname @ X @ (dom_pname_com @ F2)) = (dom_pname_com @ F2)))))). % insert_dom
thf(fact_145_insert__dom, axiom,
    ((![F2 : hoare_958474565_state > option_com, X : hoare_958474565_state, Y4 : com]: (((F2 @ X) = (some_com @ Y4)) => ((insert776267541_state @ X @ (dom_Ho256784515te_com @ F2)) = (dom_Ho256784515te_com @ F2)))))). % insert_dom
thf(fact_146_MGT__BodyN, axiom,
    ((![Pn : pname, G2 : set_Ho840737317_state]: ((hoare_604442164_state @ (insert776267541_state @ (hoare_Mirabelle_MGT @ (body2 @ Pn)) @ G2) @ (insert776267541_state @ (hoare_Mirabelle_MGT @ (the_com @ (body @ Pn))) @ bot_bo105666705_state)) => (hoare_604442164_state @ G2 @ (insert776267541_state @ (hoare_Mirabelle_MGT @ (body2 @ Pn)) @ bot_bo105666705_state)))))). % MGT_BodyN
thf(fact_147_rev__image__eqI, axiom,
    ((![X : pname, A : set_pname, B : pname, F2 : pname > pname]: ((member_pname @ X @ A) => ((B = (F2 @ X)) => (member_pname @ B @ (image_pname_pname @ F2 @ A))))))). % rev_image_eqI
thf(fact_148_rev__image__eqI, axiom,
    ((![X : pname, A : set_pname, B : hoare_958474565_state, F2 : pname > hoare_958474565_state]: ((member_pname @ X @ A) => ((B = (F2 @ X)) => (member109514606_state @ B @ (image_2144627828_state @ F2 @ A))))))). % rev_image_eqI
thf(fact_149_rev__image__eqI, axiom,
    ((![X : hoare_958474565_state, A : set_Ho840737317_state, B : pname, F2 : hoare_958474565_state > pname]: ((member109514606_state @ X @ A) => ((B = (F2 @ X)) => (member_pname @ B @ (image_871391498_pname @ F2 @ A))))))). % rev_image_eqI
thf(fact_150_rev__image__eqI, axiom,
    ((![X : hoare_958474565_state, A : set_Ho840737317_state, B : hoare_958474565_state, F2 : hoare_958474565_state > hoare_958474565_state]: ((member109514606_state @ X @ A) => ((B = (F2 @ X)) => (member109514606_state @ B @ (image_1849792670_state @ F2 @ A))))))). % rev_image_eqI
thf(fact_151_ball__imageD, axiom,
    ((![F2 : pname > hoare_958474565_state, A : set_pname, P : hoare_958474565_state > $o]: ((![X3 : hoare_958474565_state]: ((member109514606_state @ X3 @ (image_2144627828_state @ F2 @ A)) => (P @ X3))) => (![X6 : pname]: ((member_pname @ X6 @ A) => (P @ (F2 @ X6)))))))). % ball_imageD
thf(fact_152_image__cong, axiom,
    ((![M2 : set_pname, N : set_pname, F2 : pname > hoare_958474565_state, G3 : pname > hoare_958474565_state]: ((M2 = N) => ((![X3 : pname]: ((member_pname @ X3 @ N) => ((F2 @ X3) = (G3 @ X3)))) => ((image_2144627828_state @ F2 @ M2) = (image_2144627828_state @ G3 @ N))))))). % image_cong
thf(fact_153_bex__imageD, axiom,
    ((![F2 : pname > hoare_958474565_state, A : set_pname, P : hoare_958474565_state > $o]: ((?[X6 : hoare_958474565_state]: ((member109514606_state @ X6 @ (image_2144627828_state @ F2 @ A)) & (P @ X6))) => (?[X3 : pname]: ((member_pname @ X3 @ A) & (P @ (F2 @ X3)))))))). % bex_imageD
thf(fact_154_image__iff, axiom,
    ((![Z2 : hoare_958474565_state, F2 : pname > hoare_958474565_state, A : set_pname]: ((member109514606_state @ Z2 @ (image_2144627828_state @ F2 @ A)) = (?[X4 : pname]: (((member_pname @ X4 @ A)) & ((Z2 = (F2 @ X4))))))))). % image_iff
thf(fact_155_imageI, axiom,
    ((![X : pname, A : set_pname, F2 : pname > pname]: ((member_pname @ X @ A) => (member_pname @ (F2 @ X) @ (image_pname_pname @ F2 @ A)))))). % imageI
thf(fact_156_imageI, axiom,
    ((![X : pname, A : set_pname, F2 : pname > hoare_958474565_state]: ((member_pname @ X @ A) => (member109514606_state @ (F2 @ X) @ (image_2144627828_state @ F2 @ A)))))). % imageI
thf(fact_157_imageI, axiom,
    ((![X : hoare_958474565_state, A : set_Ho840737317_state, F2 : hoare_958474565_state > pname]: ((member109514606_state @ X @ A) => (member_pname @ (F2 @ X) @ (image_871391498_pname @ F2 @ A)))))). % imageI
thf(fact_158_imageI, axiom,
    ((![X : hoare_958474565_state, A : set_Ho840737317_state, F2 : hoare_958474565_state > hoare_958474565_state]: ((member109514606_state @ X @ A) => (member109514606_state @ (F2 @ X) @ (image_1849792670_state @ F2 @ A)))))). % imageI
thf(fact_159_MGF, axiom,
    ((![C : com]: (hoare_405891322gleton => (wT_bodies => ((wt @ C) => (hoare_604442164_state @ bot_bo105666705_state @ (insert776267541_state @ (hoare_Mirabelle_MGT @ C) @ bot_bo105666705_state)))))))). % MGF
thf(fact_160_Compr__image__eq, axiom,
    ((![F2 : pname > pname, A : set_pname, P : pname > $o]: ((collect_pname @ (^[X4 : pname]: (((member_pname @ X4 @ (image_pname_pname @ F2 @ A))) & ((P @ X4))))) = (image_pname_pname @ F2 @ (collect_pname @ (^[X4 : pname]: (((member_pname @ X4 @ A)) & ((P @ (F2 @ X4))))))))))). % Compr_image_eq
thf(fact_161_Compr__image__eq, axiom,
    ((![F2 : hoare_958474565_state > pname, A : set_Ho840737317_state, P : pname > $o]: ((collect_pname @ (^[X4 : pname]: (((member_pname @ X4 @ (image_871391498_pname @ F2 @ A))) & ((P @ X4))))) = (image_871391498_pname @ F2 @ (collec305460656_state @ (^[X4 : hoare_958474565_state]: (((member109514606_state @ X4 @ A)) & ((P @ (F2 @ X4))))))))))). % Compr_image_eq
thf(fact_162_Compr__image__eq, axiom,
    ((![F2 : pname > hoare_958474565_state, A : set_pname, P : hoare_958474565_state > $o]: ((collec305460656_state @ (^[X4 : hoare_958474565_state]: (((member109514606_state @ X4 @ (image_2144627828_state @ F2 @ A))) & ((P @ X4))))) = (image_2144627828_state @ F2 @ (collect_pname @ (^[X4 : pname]: (((member_pname @ X4 @ A)) & ((P @ (F2 @ X4))))))))))). % Compr_image_eq
thf(fact_163_Compr__image__eq, axiom,
    ((![F2 : hoare_958474565_state > hoare_958474565_state, A : set_Ho840737317_state, P : hoare_958474565_state > $o]: ((collec305460656_state @ (^[X4 : hoare_958474565_state]: (((member109514606_state @ X4 @ (image_1849792670_state @ F2 @ A))) & ((P @ X4))))) = (image_1849792670_state @ F2 @ (collec305460656_state @ (^[X4 : hoare_958474565_state]: (((member109514606_state @ X4 @ A)) & ((P @ (F2 @ X4))))))))))). % Compr_image_eq
thf(fact_164_image__image, axiom,
    ((![F2 : hoare_958474565_state > hoare_958474565_state, G3 : pname > hoare_958474565_state, A : set_pname]: ((image_1849792670_state @ F2 @ (image_2144627828_state @ G3 @ A)) = (image_2144627828_state @ (^[X4 : pname]: (F2 @ (G3 @ X4))) @ A))))). % image_image
thf(fact_165_image__image, axiom,
    ((![F2 : pname > hoare_958474565_state, G3 : pname > pname, A : set_pname]: ((image_2144627828_state @ F2 @ (image_pname_pname @ G3 @ A)) = (image_2144627828_state @ (^[X4 : pname]: (F2 @ (G3 @ X4))) @ A))))). % image_image
thf(fact_166_the__elem__eq, axiom,
    ((![X : hoare_958474565_state]: ((the_el1300254266_state @ (insert776267541_state @ X @ bot_bo105666705_state)) = X)))). % the_elem_eq
thf(fact_167_order__refl, axiom,
    ((![X : set_Ho840737317_state]: (ord_le1945819589_state @ X @ X)))). % order_refl
thf(fact_168_image__Collect__subsetI, axiom,
    ((![P : pname > $o, F2 : pname > hoare_958474565_state, B3 : set_Ho840737317_state]: ((![X3 : pname]: ((P @ X3) => (member109514606_state @ (F2 @ X3) @ B3))) => (ord_le1945819589_state @ (image_2144627828_state @ F2 @ (collect_pname @ P)) @ B3))))). % image_Collect_subsetI
thf(fact_169_is__singletonI, axiom,
    ((![X : hoare_958474565_state]: (is_sin536631353_state @ (insert776267541_state @ X @ bot_bo105666705_state))))). % is_singletonI
thf(fact_170_weak__Body, axiom,
    ((![G2 : set_Ho840737317_state, P : state > state > $o, Pn : pname, Q : state > state > $o]: ((hoare_604442164_state @ G2 @ (insert776267541_state @ (hoare_1659279548_state @ P @ (the_com @ (body @ Pn)) @ Q) @ bot_bo105666705_state)) => (hoare_604442164_state @ G2 @ (insert776267541_state @ (hoare_1659279548_state @ P @ (body2 @ Pn) @ Q) @ bot_bo105666705_state)))))). % weak_Body
thf(fact_171_BodyN, axiom,
    ((![P : state > state > $o, Pn : pname, Q : state > state > $o, G2 : set_Ho840737317_state]: ((hoare_604442164_state @ (insert776267541_state @ (hoare_1659279548_state @ P @ (body2 @ Pn) @ Q) @ G2) @ (insert776267541_state @ (hoare_1659279548_state @ P @ (the_com @ (body @ Pn)) @ Q) @ bot_bo105666705_state)) => (hoare_604442164_state @ G2 @ (insert776267541_state @ (hoare_1659279548_state @ P @ (body2 @ Pn) @ Q) @ bot_bo105666705_state)))))). % BodyN
thf(fact_172_insert__subsetI, axiom,
    ((![X : pname, A : set_pname, X5 : set_pname]: ((member_pname @ X @ A) => ((ord_le865024672_pname @ X5 @ A) => (ord_le865024672_pname @ (insert_pname @ X @ X5) @ A)))))). % insert_subsetI
thf(fact_173_insert__subsetI, axiom,
    ((![X : hoare_958474565_state, A : set_Ho840737317_state, X5 : set_Ho840737317_state]: ((member109514606_state @ X @ A) => ((ord_le1945819589_state @ X5 @ A) => (ord_le1945819589_state @ (insert776267541_state @ X @ X5) @ A)))))). % insert_subsetI
thf(fact_174_subset__emptyI, axiom,
    ((![A : set_pname]: ((![X3 : pname]: (~ ((member_pname @ X3 @ A)))) => (ord_le865024672_pname @ A @ bot_bot_set_pname))))). % subset_emptyI
thf(fact_175_subset__emptyI, axiom,
    ((![A : set_Ho840737317_state]: ((![X3 : hoare_958474565_state]: (~ ((member109514606_state @ X3 @ A)))) => (ord_le1945819589_state @ A @ bot_bo105666705_state))))). % subset_emptyI
thf(fact_176_all__subset__image, axiom,
    ((![F2 : pname > hoare_958474565_state, A : set_pname, P : set_Ho840737317_state > $o]: ((![B4 : set_Ho840737317_state]: (((ord_le1945819589_state @ B4 @ (image_2144627828_state @ F2 @ A))) => ((P @ B4)))) = (![B4 : set_pname]: (((ord_le865024672_pname @ B4 @ A)) => ((P @ (image_2144627828_state @ F2 @ B4))))))))). % all_subset_image
thf(fact_177_all__subset__image, axiom,
    ((![F2 : hoare_958474565_state > hoare_958474565_state, A : set_Ho840737317_state, P : set_Ho840737317_state > $o]: ((![B4 : set_Ho840737317_state]: (((ord_le1945819589_state @ B4 @ (image_1849792670_state @ F2 @ A))) => ((P @ B4)))) = (![B4 : set_Ho840737317_state]: (((ord_le1945819589_state @ B4 @ A)) => ((P @ (image_1849792670_state @ F2 @ B4))))))))). % all_subset_image
thf(fact_178_bot__set__def, axiom,
    ((bot_bo105666705_state = (collec305460656_state @ bot_bo1428770700tate_o)))). % bot_set_def
thf(fact_179_less__eq__set__def, axiom,
    ((ord_le865024672_pname = (^[A3 : set_pname]: (^[B4 : set_pname]: (ord_less_eq_pname_o @ (^[X4 : pname]: (member_pname @ X4 @ A3)) @ (^[X4 : pname]: (member_pname @ X4 @ B4)))))))). % less_eq_set_def
thf(fact_180_less__eq__set__def, axiom,
    ((ord_le1945819589_state = (^[A3 : set_Ho840737317_state]: (^[B4 : set_Ho840737317_state]: (ord_le1483368280tate_o @ (^[X4 : hoare_958474565_state]: (member109514606_state @ X4 @ A3)) @ (^[X4 : hoare_958474565_state]: (member109514606_state @ X4 @ B4)))))))). % less_eq_set_def
thf(fact_181_is__singleton__the__elem, axiom,
    ((is_sin536631353_state = (^[A3 : set_Ho840737317_state]: (A3 = (insert776267541_state @ (the_el1300254266_state @ A3) @ bot_bo105666705_state)))))). % is_singleton_the_elem
thf(fact_182_is__singletonI_H, axiom,
    ((![A : set_pname]: ((~ ((A = bot_bot_set_pname))) => ((![X3 : pname, Y : pname]: ((member_pname @ X3 @ A) => ((member_pname @ Y @ A) => (X3 = Y)))) => (is_singleton_pname @ A)))))). % is_singletonI'
thf(fact_183_is__singletonI_H, axiom,
    ((![A : set_Ho840737317_state]: ((~ ((A = bot_bo105666705_state))) => ((![X3 : hoare_958474565_state, Y : hoare_958474565_state]: ((member109514606_state @ X3 @ A) => ((member109514606_state @ Y @ A) => (X3 = Y)))) => (is_sin536631353_state @ A)))))). % is_singletonI'
thf(fact_184_dual__order_Oantisym, axiom,
    ((![B : set_Ho840737317_state, A2 : set_Ho840737317_state]: ((ord_le1945819589_state @ B @ A2) => ((ord_le1945819589_state @ A2 @ B) => (A2 = B)))))). % dual_order.antisym
thf(fact_185_dual__order_Oeq__iff, axiom,
    (((^[Y3 : set_Ho840737317_state]: (^[Z : set_Ho840737317_state]: (Y3 = Z))) = (^[A4 : set_Ho840737317_state]: (^[B6 : set_Ho840737317_state]: (((ord_le1945819589_state @ B6 @ A4)) & ((ord_le1945819589_state @ A4 @ B6)))))))). % dual_order.eq_iff
thf(fact_186_dual__order_Otrans, axiom,
    ((![B : set_Ho840737317_state, A2 : set_Ho840737317_state, C : set_Ho840737317_state]: ((ord_le1945819589_state @ B @ A2) => ((ord_le1945819589_state @ C @ B) => (ord_le1945819589_state @ C @ A2)))))). % dual_order.trans
thf(fact_187_dual__order_Orefl, axiom,
    ((![A2 : set_Ho840737317_state]: (ord_le1945819589_state @ A2 @ A2)))). % dual_order.refl
thf(fact_188_order__trans, axiom,
    ((![X : set_Ho840737317_state, Y4 : set_Ho840737317_state, Z2 : set_Ho840737317_state]: ((ord_le1945819589_state @ X @ Y4) => ((ord_le1945819589_state @ Y4 @ Z2) => (ord_le1945819589_state @ X @ Z2)))))). % order_trans
thf(fact_189_order__class_Oorder_Oantisym, axiom,
    ((![A2 : set_Ho840737317_state, B : set_Ho840737317_state]: ((ord_le1945819589_state @ A2 @ B) => ((ord_le1945819589_state @ B @ A2) => (A2 = B)))))). % order_class.order.antisym
thf(fact_190_ord__le__eq__trans, axiom,
    ((![A2 : set_Ho840737317_state, B : set_Ho840737317_state, C : set_Ho840737317_state]: ((ord_le1945819589_state @ A2 @ B) => ((B = C) => (ord_le1945819589_state @ A2 @ C)))))). % ord_le_eq_trans
thf(fact_191_ord__eq__le__trans, axiom,
    ((![A2 : set_Ho840737317_state, B : set_Ho840737317_state, C : set_Ho840737317_state]: ((A2 = B) => ((ord_le1945819589_state @ B @ C) => (ord_le1945819589_state @ A2 @ C)))))). % ord_eq_le_trans
thf(fact_192_order__class_Oorder_Oeq__iff, axiom,
    (((^[Y3 : set_Ho840737317_state]: (^[Z : set_Ho840737317_state]: (Y3 = Z))) = (^[A4 : set_Ho840737317_state]: (^[B6 : set_Ho840737317_state]: (((ord_le1945819589_state @ A4 @ B6)) & ((ord_le1945819589_state @ B6 @ A4)))))))). % order_class.order.eq_iff
thf(fact_193_antisym__conv, axiom,
    ((![Y4 : set_Ho840737317_state, X : set_Ho840737317_state]: ((ord_le1945819589_state @ Y4 @ X) => ((ord_le1945819589_state @ X @ Y4) = (X = Y4)))))). % antisym_conv
thf(fact_194_order_Otrans, axiom,
    ((![A2 : set_Ho840737317_state, B : set_Ho840737317_state, C : set_Ho840737317_state]: ((ord_le1945819589_state @ A2 @ B) => ((ord_le1945819589_state @ B @ C) => (ord_le1945819589_state @ A2 @ C)))))). % order.trans
thf(fact_195_eq__refl, axiom,
    ((![X : set_Ho840737317_state, Y4 : set_Ho840737317_state]: ((X = Y4) => (ord_le1945819589_state @ X @ Y4))))). % eq_refl
thf(fact_196_antisym, axiom,
    ((![X : set_Ho840737317_state, Y4 : set_Ho840737317_state]: ((ord_le1945819589_state @ X @ Y4) => ((ord_le1945819589_state @ Y4 @ X) => (X = Y4)))))). % antisym
thf(fact_197_eq__iff, axiom,
    (((^[Y3 : set_Ho840737317_state]: (^[Z : set_Ho840737317_state]: (Y3 = Z))) = (^[X4 : set_Ho840737317_state]: (^[Y5 : set_Ho840737317_state]: (((ord_le1945819589_state @ X4 @ Y5)) & ((ord_le1945819589_state @ Y5 @ X4)))))))). % eq_iff
thf(fact_198_ord__le__eq__subst, axiom,
    ((![A2 : set_Ho840737317_state, B : set_Ho840737317_state, F2 : set_Ho840737317_state > set_Ho840737317_state, C : set_Ho840737317_state]: ((ord_le1945819589_state @ A2 @ B) => (((F2 @ B) = C) => ((![X3 : set_Ho840737317_state, Y : set_Ho840737317_state]: ((ord_le1945819589_state @ X3 @ Y) => (ord_le1945819589_state @ (F2 @ X3) @ (F2 @ Y)))) => (ord_le1945819589_state @ (F2 @ A2) @ C))))))). % ord_le_eq_subst
thf(fact_199_ord__eq__le__subst, axiom,
    ((![A2 : set_Ho840737317_state, F2 : set_Ho840737317_state > set_Ho840737317_state, B : set_Ho840737317_state, C : set_Ho840737317_state]: ((A2 = (F2 @ B)) => ((ord_le1945819589_state @ B @ C) => ((![X3 : set_Ho840737317_state, Y : set_Ho840737317_state]: ((ord_le1945819589_state @ X3 @ Y) => (ord_le1945819589_state @ (F2 @ X3) @ (F2 @ Y)))) => (ord_le1945819589_state @ A2 @ (F2 @ C)))))))). % ord_eq_le_subst
thf(fact_200_order__subst2, axiom,
    ((![A2 : set_Ho840737317_state, B : set_Ho840737317_state, F2 : set_Ho840737317_state > set_Ho840737317_state, C : set_Ho840737317_state]: ((ord_le1945819589_state @ A2 @ B) => ((ord_le1945819589_state @ (F2 @ B) @ C) => ((![X3 : set_Ho840737317_state, Y : set_Ho840737317_state]: ((ord_le1945819589_state @ X3 @ Y) => (ord_le1945819589_state @ (F2 @ X3) @ (F2 @ Y)))) => (ord_le1945819589_state @ (F2 @ A2) @ C))))))). % order_subst2
thf(fact_201_order__subst1, axiom,
    ((![A2 : set_Ho840737317_state, F2 : set_Ho840737317_state > set_Ho840737317_state, B : set_Ho840737317_state, C : set_Ho840737317_state]: ((ord_le1945819589_state @ A2 @ (F2 @ B)) => ((ord_le1945819589_state @ B @ C) => ((![X3 : set_Ho840737317_state, Y : set_Ho840737317_state]: ((ord_le1945819589_state @ X3 @ Y) => (ord_le1945819589_state @ (F2 @ X3) @ (F2 @ Y)))) => (ord_le1945819589_state @ A2 @ (F2 @ C)))))))). % order_subst1

% Conjectures (5)
thf(conj_0, hypothesis,
    (hoare_405891322gleton)).
thf(conj_1, hypothesis,
    (wT_bodies)).
thf(conj_2, hypothesis,
    ((wt @ c))).
thf(conj_3, hypothesis,
    (((body @ pn) = (some_com @ y)))).
thf(conj_4, conjecture,
    ((hoare_604442164_state @ (image_2144627828_state @ (^[Pn2 : pname]: (hoare_Mirabelle_MGT @ (body2 @ Pn2))) @ (dom_pname_com @ body)) @ (image_2144627828_state @ (^[Pn2 : pname]: (hoare_Mirabelle_MGT @ (the_com @ (body @ Pn2)))) @ (dom_pname_com @ body))))).
