% 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_460__3254890_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:15:09.099

% 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 (31)
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_Finite__Set_Ofinite_001t__Com__Opname, type,
    finite_finite_pname : set_pname > $o).
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_Lattices_Osup__class_Osup_001_062_It__Hoare____Mirabelle____raqjowkjvm__Otriple_It__Com__Ostate_J_M_Eo_J, type,
    sup_su2044190244tate_o : (hoare_958474565_state > $o) > (hoare_958474565_state > $o) > hoare_958474565_state > $o).
thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Com__Opname_J, type,
    sup_sup_set_pname : set_pname > set_pname > set_pname).
thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Hoare____Mirabelle____raqjowkjvm__Otriple_It__Com__Ostate_J_J, type,
    sup_su737426425_state : set_Ho840737317_state > set_Ho840737317_state > set_Ho840737317_state).
thf(sy_c_Map_Odom_001t__Com__Opname_001t__Com__Ocom, type,
    dom_pname_com : (pname > option_com) > set_pname).
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_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__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_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 (140)
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_empty, axiom,
    ((![G2 : set_Ho840737317_state]: (hoare_604442164_state @ G2 @ bot_bo105666705_state)))). % empty
thf(fact_3_state__not__singleton__def, axiom,
    ((hoare_405891322gleton = (?[S2 : state]: (?[T2 : state]: (~ ((S2 = T2)))))))). % state_not_singleton_def
thf(fact_4_WT__bodiesD, axiom,
    ((![Pn : pname, B : com]: (wT_bodies => (((body @ Pn) = (some_com @ B)) => (wt @ B)))))). % WT_bodiesD
thf(fact_5_WTs__elim__cases_I7_J, axiom,
    ((![P : pname]: ((wt @ (body2 @ P)) => (~ ((![Y : com]: (~ (((body @ P) = (some_com @ Y))))))))))). % WTs_elim_cases(7)
thf(fact_6_Un__empty, axiom,
    ((![A : set_Ho840737317_state, B2 : set_Ho840737317_state]: (((sup_su737426425_state @ A @ B2) = bot_bo105666705_state) = (((A = bot_bo105666705_state)) & ((B2 = bot_bo105666705_state))))))). % Un_empty
thf(fact_7_sup__bot__left, axiom,
    ((![X : set_Ho840737317_state]: ((sup_su737426425_state @ bot_bo105666705_state @ X) = X)))). % sup_bot_left
thf(fact_8_sup__bot__right, axiom,
    ((![X : set_Ho840737317_state]: ((sup_su737426425_state @ X @ bot_bo105666705_state) = X)))). % sup_bot_right
thf(fact_9_bot__eq__sup__iff, axiom,
    ((![X : set_Ho840737317_state, Y2 : set_Ho840737317_state]: ((bot_bo105666705_state = (sup_su737426425_state @ X @ Y2)) = (((X = bot_bo105666705_state)) & ((Y2 = bot_bo105666705_state))))))). % bot_eq_sup_iff
thf(fact_10_sup__eq__bot__iff, axiom,
    ((![X : set_Ho840737317_state, Y2 : set_Ho840737317_state]: (((sup_su737426425_state @ X @ Y2) = bot_bo105666705_state) = (((X = bot_bo105666705_state)) & ((Y2 = bot_bo105666705_state))))))). % sup_eq_bot_iff
thf(fact_11_sup__bot_Oeq__neutr__iff, axiom,
    ((![A2 : set_Ho840737317_state, B : set_Ho840737317_state]: (((sup_su737426425_state @ A2 @ B) = bot_bo105666705_state) = (((A2 = bot_bo105666705_state)) & ((B = bot_bo105666705_state))))))). % sup_bot.eq_neutr_iff
thf(fact_12_sup__bot_Oleft__neutral, axiom,
    ((![A2 : set_Ho840737317_state]: ((sup_su737426425_state @ bot_bo105666705_state @ A2) = A2)))). % sup_bot.left_neutral
thf(fact_13_sup__bot_Oneutr__eq__iff, axiom,
    ((![A2 : set_Ho840737317_state, B : set_Ho840737317_state]: ((bot_bo105666705_state = (sup_su737426425_state @ A2 @ B)) = (((A2 = bot_bo105666705_state)) & ((B = bot_bo105666705_state))))))). % sup_bot.neutr_eq_iff
thf(fact_14_sup__bot_Oright__neutral, axiom,
    ((![A2 : set_Ho840737317_state]: ((sup_su737426425_state @ A2 @ bot_bo105666705_state) = A2)))). % sup_bot.right_neutral
thf(fact_15_image__empty, axiom,
    ((![F : pname > hoare_958474565_state]: ((image_2144627828_state @ F @ bot_bot_set_pname) = bot_bo105666705_state)))). % image_empty
thf(fact_16_image__empty, axiom,
    ((![F : hoare_958474565_state > hoare_958474565_state]: ((image_1849792670_state @ F @ bot_bo105666705_state) = bot_bo105666705_state)))). % image_empty
thf(fact_17_image__eqI, axiom,
    ((![B : hoare_958474565_state, F : pname > hoare_958474565_state, X : pname, A : set_pname]: ((B = (F @ X)) => ((member_pname @ X @ A) => (member109514606_state @ B @ (image_2144627828_state @ F @ A))))))). % image_eqI
thf(fact_18_empty__Collect__eq, axiom,
    ((![P : hoare_958474565_state > $o]: ((bot_bo105666705_state = (collec305460656_state @ P)) = (![X2 : hoare_958474565_state]: (~ ((P @ X2)))))))). % empty_Collect_eq
thf(fact_19_Collect__empty__eq, axiom,
    ((![P : hoare_958474565_state > $o]: (((collec305460656_state @ P) = bot_bo105666705_state) = (![X2 : hoare_958474565_state]: (~ ((P @ X2)))))))). % Collect_empty_eq
thf(fact_20_all__not__in__conv, axiom,
    ((![A : set_Ho840737317_state]: ((![X2 : hoare_958474565_state]: (~ ((member109514606_state @ X2 @ A)))) = (A = bot_bo105666705_state))))). % all_not_in_conv
thf(fact_21_empty__iff, axiom,
    ((![C : hoare_958474565_state]: (~ ((member109514606_state @ C @ bot_bo105666705_state)))))). % empty_iff
thf(fact_22_sup_Oright__idem, axiom,
    ((![A2 : set_Ho840737317_state, B : set_Ho840737317_state]: ((sup_su737426425_state @ (sup_su737426425_state @ A2 @ B) @ B) = (sup_su737426425_state @ A2 @ B))))). % sup.right_idem
thf(fact_23_sup__left__idem, axiom,
    ((![X : set_Ho840737317_state, Y2 : set_Ho840737317_state]: ((sup_su737426425_state @ X @ (sup_su737426425_state @ X @ Y2)) = (sup_su737426425_state @ X @ Y2))))). % sup_left_idem
thf(fact_24_sup_Oleft__idem, axiom,
    ((![A2 : set_Ho840737317_state, B : set_Ho840737317_state]: ((sup_su737426425_state @ A2 @ (sup_su737426425_state @ A2 @ B)) = (sup_su737426425_state @ A2 @ B))))). % sup.left_idem
thf(fact_25_sup__idem, axiom,
    ((![X : set_Ho840737317_state]: ((sup_su737426425_state @ X @ X) = X)))). % sup_idem
thf(fact_26_sup_Oidem, axiom,
    ((![A2 : set_Ho840737317_state]: ((sup_su737426425_state @ A2 @ A2) = A2)))). % sup.idem
thf(fact_27_Un__iff, axiom,
    ((![C : hoare_958474565_state, A : set_Ho840737317_state, B2 : set_Ho840737317_state]: ((member109514606_state @ C @ (sup_su737426425_state @ A @ B2)) = (((member109514606_state @ C @ A)) | ((member109514606_state @ C @ B2))))))). % Un_iff
thf(fact_28_UnCI, axiom,
    ((![C : hoare_958474565_state, B2 : set_Ho840737317_state, A : set_Ho840737317_state]: (((~ ((member109514606_state @ C @ B2))) => (member109514606_state @ C @ A)) => (member109514606_state @ C @ (sup_su737426425_state @ A @ B2)))))). % UnCI
thf(fact_29_com_Oinject_I6_J, axiom,
    ((![X7 : pname, Y7 : pname]: (((body2 @ X7) = (body2 @ Y7)) = (X7 = Y7))))). % com.inject(6)
thf(fact_30_image__is__empty, axiom,
    ((![F : pname > hoare_958474565_state, A : set_pname]: (((image_2144627828_state @ F @ A) = bot_bo105666705_state) = (A = bot_bot_set_pname))))). % image_is_empty
thf(fact_31_image__is__empty, axiom,
    ((![F : hoare_958474565_state > hoare_958474565_state, A : set_Ho840737317_state]: (((image_1849792670_state @ F @ A) = bot_bo105666705_state) = (A = bot_bo105666705_state))))). % image_is_empty
thf(fact_32_empty__is__image, axiom,
    ((![F : pname > hoare_958474565_state, A : set_pname]: ((bot_bo105666705_state = (image_2144627828_state @ F @ A)) = (A = bot_bot_set_pname))))). % empty_is_image
thf(fact_33_empty__is__image, axiom,
    ((![F : hoare_958474565_state > hoare_958474565_state, A : set_Ho840737317_state]: ((bot_bo105666705_state = (image_1849792670_state @ F @ A)) = (A = bot_bo105666705_state))))). % empty_is_image
thf(fact_34_bot__set__def, axiom,
    ((bot_bo105666705_state = (collec305460656_state @ bot_bo1428770700tate_o)))). % bot_set_def
thf(fact_35_sup__set__def, axiom,
    ((sup_su737426425_state = (^[A3 : set_Ho840737317_state]: (^[B3 : set_Ho840737317_state]: (collec305460656_state @ (sup_su2044190244tate_o @ (^[X2 : hoare_958474565_state]: (member109514606_state @ X2 @ A3)) @ (^[X2 : hoare_958474565_state]: (member109514606_state @ X2 @ B3))))))))). % sup_set_def
thf(fact_36_rev__image__eqI, axiom,
    ((![X : pname, A : set_pname, B : hoare_958474565_state, F : pname > hoare_958474565_state]: ((member_pname @ X @ A) => ((B = (F @ X)) => (member109514606_state @ B @ (image_2144627828_state @ F @ A))))))). % rev_image_eqI
thf(fact_37_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_38_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_39_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_40_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_41_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_42_ex__in__conv, axiom,
    ((![A : set_Ho840737317_state]: ((?[X2 : hoare_958474565_state]: (member109514606_state @ X2 @ A)) = (~ ((A = bot_bo105666705_state))))))). % ex_in_conv
thf(fact_43_equals0I, axiom,
    ((![A : set_Ho840737317_state]: ((![Y : hoare_958474565_state]: (~ ((member109514606_state @ Y @ A)))) => (A = bot_bo105666705_state))))). % equals0I
thf(fact_44_equals0D, axiom,
    ((![A : set_Ho840737317_state, A2 : hoare_958474565_state]: ((A = bot_bo105666705_state) => (~ ((member109514606_state @ A2 @ A))))))). % equals0D
thf(fact_45_emptyE, axiom,
    ((![A2 : hoare_958474565_state]: (~ ((member109514606_state @ A2 @ bot_bo105666705_state)))))). % emptyE
thf(fact_46_sup__left__commute, axiom,
    ((![X : set_Ho840737317_state, Y2 : set_Ho840737317_state, Z : set_Ho840737317_state]: ((sup_su737426425_state @ X @ (sup_su737426425_state @ Y2 @ Z)) = (sup_su737426425_state @ Y2 @ (sup_su737426425_state @ X @ Z)))))). % sup_left_commute
thf(fact_47_sup_Oleft__commute, axiom,
    ((![B : set_Ho840737317_state, A2 : set_Ho840737317_state, C : set_Ho840737317_state]: ((sup_su737426425_state @ B @ (sup_su737426425_state @ A2 @ C)) = (sup_su737426425_state @ A2 @ (sup_su737426425_state @ B @ C)))))). % sup.left_commute
thf(fact_48_sup__commute, axiom,
    ((sup_su737426425_state = (^[X2 : set_Ho840737317_state]: (^[Y3 : set_Ho840737317_state]: (sup_su737426425_state @ Y3 @ X2)))))). % sup_commute
thf(fact_49_sup_Ocommute, axiom,
    ((sup_su737426425_state = (^[A4 : set_Ho840737317_state]: (^[B4 : set_Ho840737317_state]: (sup_su737426425_state @ B4 @ A4)))))). % sup.commute
thf(fact_50_sup__assoc, axiom,
    ((![X : set_Ho840737317_state, Y2 : set_Ho840737317_state, Z : set_Ho840737317_state]: ((sup_su737426425_state @ (sup_su737426425_state @ X @ Y2) @ Z) = (sup_su737426425_state @ X @ (sup_su737426425_state @ Y2 @ Z)))))). % sup_assoc
thf(fact_51_sup_Oassoc, axiom,
    ((![A2 : set_Ho840737317_state, B : set_Ho840737317_state, C : set_Ho840737317_state]: ((sup_su737426425_state @ (sup_su737426425_state @ A2 @ B) @ C) = (sup_su737426425_state @ A2 @ (sup_su737426425_state @ B @ C)))))). % sup.assoc
thf(fact_52_boolean__algebra__cancel_Osup2, axiom,
    ((![B2 : set_Ho840737317_state, K : set_Ho840737317_state, B : set_Ho840737317_state, A2 : set_Ho840737317_state]: ((B2 = (sup_su737426425_state @ K @ B)) => ((sup_su737426425_state @ A2 @ B2) = (sup_su737426425_state @ K @ (sup_su737426425_state @ A2 @ B))))))). % boolean_algebra_cancel.sup2
thf(fact_53_boolean__algebra__cancel_Osup1, axiom,
    ((![A : set_Ho840737317_state, K : set_Ho840737317_state, A2 : set_Ho840737317_state, B : set_Ho840737317_state]: ((A = (sup_su737426425_state @ K @ A2)) => ((sup_su737426425_state @ A @ B) = (sup_su737426425_state @ K @ (sup_su737426425_state @ A2 @ B))))))). % boolean_algebra_cancel.sup1
thf(fact_54_inf__sup__aci_I5_J, axiom,
    ((sup_su737426425_state = (^[X2 : set_Ho840737317_state]: (^[Y3 : set_Ho840737317_state]: (sup_su737426425_state @ Y3 @ X2)))))). % inf_sup_aci(5)
thf(fact_55_inf__sup__aci_I6_J, axiom,
    ((![X : set_Ho840737317_state, Y2 : set_Ho840737317_state, Z : set_Ho840737317_state]: ((sup_su737426425_state @ (sup_su737426425_state @ X @ Y2) @ Z) = (sup_su737426425_state @ X @ (sup_su737426425_state @ Y2 @ Z)))))). % inf_sup_aci(6)
thf(fact_56_inf__sup__aci_I7_J, axiom,
    ((![X : set_Ho840737317_state, Y2 : set_Ho840737317_state, Z : set_Ho840737317_state]: ((sup_su737426425_state @ X @ (sup_su737426425_state @ Y2 @ Z)) = (sup_su737426425_state @ Y2 @ (sup_su737426425_state @ X @ Z)))))). % inf_sup_aci(7)
thf(fact_57_inf__sup__aci_I8_J, axiom,
    ((![X : set_Ho840737317_state, Y2 : set_Ho840737317_state]: ((sup_su737426425_state @ X @ (sup_su737426425_state @ X @ Y2)) = (sup_su737426425_state @ X @ Y2))))). % inf_sup_aci(8)
thf(fact_58_Un__left__commute, axiom,
    ((![A : set_Ho840737317_state, B2 : set_Ho840737317_state, C2 : set_Ho840737317_state]: ((sup_su737426425_state @ A @ (sup_su737426425_state @ B2 @ C2)) = (sup_su737426425_state @ B2 @ (sup_su737426425_state @ A @ C2)))))). % Un_left_commute
thf(fact_59_Un__left__absorb, axiom,
    ((![A : set_Ho840737317_state, B2 : set_Ho840737317_state]: ((sup_su737426425_state @ A @ (sup_su737426425_state @ A @ B2)) = (sup_su737426425_state @ A @ B2))))). % Un_left_absorb
thf(fact_60_Un__commute, axiom,
    ((sup_su737426425_state = (^[A3 : set_Ho840737317_state]: (^[B3 : set_Ho840737317_state]: (sup_su737426425_state @ B3 @ A3)))))). % Un_commute
thf(fact_61_Un__absorb, axiom,
    ((![A : set_Ho840737317_state]: ((sup_su737426425_state @ A @ A) = A)))). % Un_absorb
thf(fact_62_Un__assoc, axiom,
    ((![A : set_Ho840737317_state, B2 : set_Ho840737317_state, C2 : set_Ho840737317_state]: ((sup_su737426425_state @ (sup_su737426425_state @ A @ B2) @ C2) = (sup_su737426425_state @ A @ (sup_su737426425_state @ B2 @ C2)))))). % Un_assoc
thf(fact_63_ball__Un, axiom,
    ((![A : set_Ho840737317_state, B2 : set_Ho840737317_state, P : hoare_958474565_state > $o]: ((![X2 : hoare_958474565_state]: (((member109514606_state @ X2 @ (sup_su737426425_state @ A @ B2))) => ((P @ X2)))) = (((![X2 : hoare_958474565_state]: (((member109514606_state @ X2 @ A)) => ((P @ X2))))) & ((![X2 : hoare_958474565_state]: (((member109514606_state @ X2 @ B2)) => ((P @ X2)))))))))). % ball_Un
thf(fact_64_bex__Un, axiom,
    ((![A : set_Ho840737317_state, B2 : set_Ho840737317_state, P : hoare_958474565_state > $o]: ((?[X2 : hoare_958474565_state]: (((member109514606_state @ X2 @ (sup_su737426425_state @ A @ B2))) & ((P @ X2)))) = (((?[X2 : hoare_958474565_state]: (((member109514606_state @ X2 @ A)) & ((P @ X2))))) | ((?[X2 : hoare_958474565_state]: (((member109514606_state @ X2 @ B2)) & ((P @ X2)))))))))). % bex_Un
thf(fact_65_UnI2, axiom,
    ((![C : hoare_958474565_state, B2 : set_Ho840737317_state, A : set_Ho840737317_state]: ((member109514606_state @ C @ B2) => (member109514606_state @ C @ (sup_su737426425_state @ A @ B2)))))). % UnI2
thf(fact_66_UnI1, axiom,
    ((![C : hoare_958474565_state, A : set_Ho840737317_state, B2 : set_Ho840737317_state]: ((member109514606_state @ C @ A) => (member109514606_state @ C @ (sup_su737426425_state @ A @ B2)))))). % UnI1
thf(fact_67_UnE, axiom,
    ((![C : hoare_958474565_state, A : set_Ho840737317_state, B2 : set_Ho840737317_state]: ((member109514606_state @ C @ (sup_su737426425_state @ A @ B2)) => ((~ ((member109514606_state @ C @ A))) => (member109514606_state @ C @ B2)))))). % UnE
thf(fact_68_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_69_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_70_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_71_imageE, axiom,
    ((![B : hoare_958474565_state, F : pname > hoare_958474565_state, A : set_pname]: ((member109514606_state @ B @ (image_2144627828_state @ F @ A)) => (~ ((![X3 : pname]: ((B = (F @ X3)) => (~ ((member_pname @ X3 @ A))))))))))). % imageE
thf(fact_72_empty__def, axiom,
    ((bot_bo105666705_state = (collec305460656_state @ (^[X2 : hoare_958474565_state]: $false))))). % empty_def
thf(fact_73_Collect__disj__eq, axiom,
    ((![P : hoare_958474565_state > $o, Q : hoare_958474565_state > $o]: ((collec305460656_state @ (^[X2 : hoare_958474565_state]: (((P @ X2)) | ((Q @ X2))))) = (sup_su737426425_state @ (collec305460656_state @ P) @ (collec305460656_state @ Q)))))). % Collect_disj_eq
thf(fact_74_Un__def, axiom,
    ((sup_su737426425_state = (^[A3 : set_Ho840737317_state]: (^[B3 : set_Ho840737317_state]: (collec305460656_state @ (^[X2 : hoare_958474565_state]: (((member109514606_state @ X2 @ A3)) | ((member109514606_state @ X2 @ B3)))))))))). % Un_def
thf(fact_75_image__Un, axiom,
    ((![F : pname > hoare_958474565_state, A : set_pname, B2 : set_pname]: ((image_2144627828_state @ F @ (sup_sup_set_pname @ A @ B2)) = (sup_su737426425_state @ (image_2144627828_state @ F @ A) @ (image_2144627828_state @ F @ B2)))))). % image_Un
thf(fact_76_image__Un, axiom,
    ((![F : hoare_958474565_state > hoare_958474565_state, A : set_Ho840737317_state, B2 : set_Ho840737317_state]: ((image_1849792670_state @ F @ (sup_su737426425_state @ A @ B2)) = (sup_su737426425_state @ (image_1849792670_state @ F @ A) @ (image_1849792670_state @ F @ B2)))))). % image_Un
thf(fact_77_Un__empty__right, axiom,
    ((![A : set_Ho840737317_state]: ((sup_su737426425_state @ A @ bot_bo105666705_state) = A)))). % Un_empty_right
thf(fact_78_Un__empty__left, axiom,
    ((![B2 : set_Ho840737317_state]: ((sup_su737426425_state @ bot_bo105666705_state @ B2) = B2)))). % Un_empty_left
thf(fact_79_MGF__lemma2__simult, axiom,
    ((![F2 : set_Ho840737317_state]: (hoare_405891322gleton => (wT_bodies => ((ord_le1945819589_state @ F2 @ (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)) @ F2))))))). % MGF_lemma2_simult
thf(fact_80_MGT__Body, axiom,
    ((![G2 : set_Ho840737317_state, Procs : set_pname]: ((hoare_604442164_state @ (sup_su737426425_state @ G2 @ (image_2144627828_state @ (^[Pn2 : pname]: (hoare_Mirabelle_MGT @ (body2 @ Pn2))) @ Procs)) @ (image_2144627828_state @ (^[Pn2 : pname]: (hoare_Mirabelle_MGT @ (the_com @ (body @ Pn2)))) @ Procs)) => ((finite_finite_pname @ Procs) => (hoare_604442164_state @ G2 @ (image_2144627828_state @ (^[Pn2 : pname]: (hoare_Mirabelle_MGT @ (body2 @ Pn2))) @ Procs))))))). % MGT_Body
thf(fact_81_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_82_option_Oinject, axiom,
    ((![X22 : com, Y22 : com]: (((some_com @ X22) = (some_com @ Y22)) = (X22 = Y22))))). % option.inject
thf(fact_83_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_84_hoare__derivs_OBody, axiom,
    ((![G2 : set_Ho840737317_state, P : pname > state > state > $o, Q : pname > state > state > $o, Procs : set_pname]: ((hoare_604442164_state @ (sup_su737426425_state @ G2 @ (image_2144627828_state @ (^[P2 : pname]: (hoare_1659279548_state @ (P @ P2) @ (body2 @ P2) @ (Q @ P2))) @ Procs)) @ (image_2144627828_state @ (^[P2 : pname]: (hoare_1659279548_state @ (P @ P2) @ (the_com @ (body @ P2)) @ (Q @ P2))) @ Procs)) => (hoare_604442164_state @ G2 @ (image_2144627828_state @ (^[P2 : pname]: (hoare_1659279548_state @ (P @ P2) @ (body2 @ P2) @ (Q @ P2))) @ Procs)))))). % hoare_derivs.Body
thf(fact_85_option_Osel, axiom,
    ((![X22 : com]: ((the_com @ (some_com @ X22)) = X22)))). % option.sel
thf(fact_86_domI, axiom,
    ((![M2 : pname > option_com, A2 : pname, B : com]: (((M2 @ A2) = (some_com @ B)) => (member_pname @ A2 @ (dom_pname_com @ M2)))))). % domI
thf(fact_87_order__refl, axiom,
    ((![X : set_Ho840737317_state]: (ord_le1945819589_state @ X @ X)))). % order_refl
thf(fact_88_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_89_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_90_insertCI, axiom,
    ((![A2 : hoare_958474565_state, B2 : set_Ho840737317_state, B : hoare_958474565_state]: (((~ ((member109514606_state @ A2 @ B2))) => (A2 = B)) => (member109514606_state @ A2 @ (insert776267541_state @ B @ B2)))))). % insertCI
thf(fact_91_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_92_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_93_le__sup__iff, axiom,
    ((![X : set_Ho840737317_state, Y2 : set_Ho840737317_state, Z : set_Ho840737317_state]: ((ord_le1945819589_state @ (sup_su737426425_state @ X @ Y2) @ Z) = (((ord_le1945819589_state @ X @ Z)) & ((ord_le1945819589_state @ Y2 @ Z))))))). % le_sup_iff
thf(fact_94_sup_Obounded__iff, axiom,
    ((![B : set_Ho840737317_state, C : set_Ho840737317_state, A2 : set_Ho840737317_state]: ((ord_le1945819589_state @ (sup_su737426425_state @ B @ C) @ A2) = (((ord_le1945819589_state @ B @ A2)) & ((ord_le1945819589_state @ C @ A2))))))). % sup.bounded_iff
thf(fact_95_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_96_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_97_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_98_subset__empty, axiom,
    ((![A : set_Ho840737317_state]: ((ord_le1945819589_state @ A @ bot_bo105666705_state) = (A = bot_bo105666705_state))))). % subset_empty
thf(fact_99_empty__subsetI, axiom,
    ((![A : set_Ho840737317_state]: (ord_le1945819589_state @ bot_bo105666705_state @ A)))). % empty_subsetI
thf(fact_100_singletonI, axiom,
    ((![A2 : hoare_958474565_state]: (member109514606_state @ A2 @ (insert776267541_state @ A2 @ bot_bo105666705_state))))). % singletonI
thf(fact_101_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_102_Un__subset__iff, axiom,
    ((![A : set_Ho840737317_state, B2 : set_Ho840737317_state, C2 : set_Ho840737317_state]: ((ord_le1945819589_state @ (sup_su737426425_state @ A @ B2) @ C2) = (((ord_le1945819589_state @ A @ C2)) & ((ord_le1945819589_state @ B2 @ C2))))))). % Un_subset_iff
thf(fact_103_Un__insert__left, axiom,
    ((![A2 : hoare_958474565_state, B2 : set_Ho840737317_state, C2 : set_Ho840737317_state]: ((sup_su737426425_state @ (insert776267541_state @ A2 @ B2) @ C2) = (insert776267541_state @ A2 @ (sup_su737426425_state @ B2 @ C2)))))). % Un_insert_left
thf(fact_104_Un__insert__right, axiom,
    ((![A : set_Ho840737317_state, A2 : hoare_958474565_state, B2 : set_Ho840737317_state]: ((sup_su737426425_state @ A @ (insert776267541_state @ A2 @ B2)) = (insert776267541_state @ A2 @ (sup_su737426425_state @ A @ B2)))))). % Un_insert_right
thf(fact_105_singleton__conv, axiom,
    ((![A2 : hoare_958474565_state]: ((collec305460656_state @ (^[X2 : hoare_958474565_state]: (X2 = A2))) = (insert776267541_state @ A2 @ bot_bo105666705_state))))). % singleton_conv
thf(fact_106_singleton__conv2, axiom,
    ((![A2 : hoare_958474565_state]: ((collec305460656_state @ ((^[Y4 : hoare_958474565_state]: (^[Z2 : hoare_958474565_state]: (Y4 = Z2))) @ A2)) = (insert776267541_state @ A2 @ bot_bo105666705_state))))). % singleton_conv2
thf(fact_107_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_108_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_109_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_110_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_111_subsetD, axiom,
    ((![A : set_Ho840737317_state, B2 : set_Ho840737317_state, C : hoare_958474565_state]: ((ord_le1945819589_state @ A @ B2) => ((member109514606_state @ C @ A) => (member109514606_state @ C @ B2)))))). % subsetD
thf(fact_112_insertI1, axiom,
    ((![A2 : hoare_958474565_state, B2 : set_Ho840737317_state]: (member109514606_state @ A2 @ (insert776267541_state @ A2 @ B2))))). % insertI1
thf(fact_113_insertI2, axiom,
    ((![A2 : hoare_958474565_state, B2 : set_Ho840737317_state, B : hoare_958474565_state]: ((member109514606_state @ A2 @ B2) => (member109514606_state @ A2 @ (insert776267541_state @ B @ B2)))))). % insertI2
thf(fact_114_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_115_subset__eq, axiom,
    ((ord_le1945819589_state = (^[A3 : set_Ho840737317_state]: (^[B3 : set_Ho840737317_state]: (![X2 : hoare_958474565_state]: (((member109514606_state @ X2 @ A3)) => ((member109514606_state @ X2 @ B3))))))))). % subset_eq
thf(fact_116_equalityD1, axiom,
    ((![A : set_Ho840737317_state, B2 : set_Ho840737317_state]: ((A = B2) => (ord_le1945819589_state @ A @ B2))))). % equalityD1
thf(fact_117_equalityD2, axiom,
    ((![A : set_Ho840737317_state, B2 : set_Ho840737317_state]: ((A = B2) => (ord_le1945819589_state @ B2 @ A))))). % equalityD2
thf(fact_118_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_119_subset__iff, axiom,
    ((ord_le1945819589_state = (^[A3 : set_Ho840737317_state]: (^[B3 : set_Ho840737317_state]: (![T2 : hoare_958474565_state]: (((member109514606_state @ T2 @ A3)) => ((member109514606_state @ T2 @ B3))))))))). % subset_iff
thf(fact_120_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_121_subset__refl, axiom,
    ((![A : set_Ho840737317_state]: (ord_le1945819589_state @ A @ A)))). % subset_refl
thf(fact_122_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_123_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_124_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_125_insert__absorb, axiom,
    ((![A2 : hoare_958474565_state, A : set_Ho840737317_state]: ((member109514606_state @ A2 @ A) => ((insert776267541_state @ A2 @ A) = A))))). % insert_absorb
thf(fact_126_insert__eq__iff, axiom,
    ((![A2 : hoare_958474565_state, A : set_Ho840737317_state, B : hoare_958474565_state, B2 : set_Ho840737317_state]: ((~ ((member109514606_state @ A2 @ A))) => ((~ ((member109514606_state @ B @ B2))) => (((insert776267541_state @ A2 @ A) = (insert776267541_state @ B @ B2)) = (((((A2 = B)) => ((A = B2)))) & ((((~ ((A2 = B)))) => ((?[C3 : set_Ho840737317_state]: (((A = (insert776267541_state @ B @ C3))) & ((((~ ((member109514606_state @ B @ C3)))) & ((((B2 = (insert776267541_state @ A2 @ C3))) & ((~ ((member109514606_state @ A2 @ C3)))))))))))))))))))). % insert_eq_iff
thf(fact_127_set__eq__subset, axiom,
    (((^[Y4 : set_Ho840737317_state]: (^[Z2 : set_Ho840737317_state]: (Y4 = Z2))) = (^[A3 : set_Ho840737317_state]: (^[B3 : set_Ho840737317_state]: (((ord_le1945819589_state @ A3 @ B3)) & ((ord_le1945819589_state @ B3 @ A3)))))))). % set_eq_subset
thf(fact_128_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_129_insert__commute, axiom,
    ((![X : hoare_958474565_state, Y2 : hoare_958474565_state, A : set_Ho840737317_state]: ((insert776267541_state @ X @ (insert776267541_state @ Y2 @ A)) = (insert776267541_state @ Y2 @ (insert776267541_state @ X @ A)))))). % insert_commute
thf(fact_130_subset__insertI, axiom,
    ((![B2 : set_Ho840737317_state, A2 : hoare_958474565_state]: (ord_le1945819589_state @ B2 @ (insert776267541_state @ A2 @ B2))))). % subset_insertI
thf(fact_131_subset__insertI2, axiom,
    ((![A : set_Ho840737317_state, B2 : set_Ho840737317_state, B : hoare_958474565_state]: ((ord_le1945819589_state @ A @ B2) => (ord_le1945819589_state @ A @ (insert776267541_state @ B @ B2)))))). % subset_insertI2
thf(fact_132_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_133_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_134_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_135_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_136_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_137_dual__order_Oeq__iff, axiom,
    (((^[Y4 : set_Ho840737317_state]: (^[Z2 : set_Ho840737317_state]: (Y4 = Z2))) = (^[A4 : set_Ho840737317_state]: (^[B4 : set_Ho840737317_state]: (((ord_le1945819589_state @ B4 @ A4)) & ((ord_le1945819589_state @ A4 @ B4)))))))). % dual_order.eq_iff
thf(fact_138_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_139_dual__order_Orefl, axiom,
    ((![A2 : set_Ho840737317_state]: (ord_le1945819589_state @ A2 @ A2)))). % dual_order.refl

% 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 @ (sup_su737426425_state @ bot_bo105666705_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))))).
