fof(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2,axiom,![X0_2E0, X1_2E0]: ((p(s(tyop_2Emin_2Ebool,X0_2E0)) & p(s(tyop_2Emin_2Ebool,X1_2E0))) <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_2F_5C_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))))).
fof(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2,axiom,![X0_2E0, X1_2E0]: ((p(s(tyop_2Emin_2Ebool,X0_2E0)) | p(s(tyop_2Emin_2Ebool,X1_2E0))) <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_5C_2F_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))))).
fof(arityeq1_2Ec_2Ebool_2E_7E_2E1,axiom,![X0_2E0]: (~ (p(s(tyop_2Emin_2Ebool,X0_2E0))) <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Ebool,X0_2E0)))))).
fof(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2,axiom,![X0_2E0, X1_2E0]: ((p(s(tyop_2Emin_2Ebool,X0_2E0)) => p(s(tyop_2Emin_2Ebool,X1_2E0))) <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_3D_3E_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))))).
fof(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0, X1_2E0]: ((s(A_27a,X0_2E0) = s(A_27a,X1_2E0)) <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0)))))).
fof(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0]: (s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_21_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))))).
fof(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0]: (s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_3F_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))))).
fof(arityeq1_2Ec_2Efmaptree_2Ewf_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,![A_27a, A_27b]: ![X0_2E0]: (s(tyop_2Emin_2Ebool,c_2Efmaptree_2Ewf_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Eoption_2Eoption(A_27a)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),c_2Efmaptree_2Ewf_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Eoption_2Eoption(A_27a)),X0_2E0))))).
fof(arityeq2_2Ec_2Efinite__map_2EFAPPLY_2E2_2Emono_2EA_27b_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28A_27b_29_2Ctyop_2Eoption_2Eoption_28A_27a_29_29,axiom,![A_27a, A_27b]: ![X0_2E0, X1_2E0]: (s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Eoption_2Eoption(A_27a)),c_2Efinite__map_2EFAPPLY_2E2(s(tyop_2Efinite__map_2Efmap(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Eoption_2Eoption(A_27a))),X0_2E0),s(A_27b,X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Eoption_2Eoption(A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Eoption_2Eoption(A_27a)))),c_2Efinite__map_2EFAPPLY_2E0),s(tyop_2Efinite__map_2Efmap(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Eoption_2Eoption(A_27a))),X0_2E0))),s(A_27b,X1_2E0))))).
fof(arityeq2_2Ec_2Efmaptree_2Econstruct_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,![A_27a, A_27b]: ![X0_2E0, X1_2E0]: (s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Eoption_2Eoption(A_27a)),c_2Efmaptree_2Econstruct_2E2(s(A_27a,X0_2E0),s(tyop_2Efinite__map_2Efmap(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Eoption_2Eoption(A_27a))),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Eoption_2Eoption(A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Eoption_2Eoption(A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Eoption_2Eoption(A_27a)))),c_2Efmaptree_2Econstruct_2E0),s(A_27a,X0_2E0))),s(tyop_2Efinite__map_2Efmap(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Eoption_2Eoption(A_27a))),X1_2E0))))).
fof(arityeq1_2Ec_2Efinite__map_2EFDOM_2E1_2Emono_2EA_27b_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28A_27b_29_2Ctyop_2Eoption_2Eoption_28A_27a_29_29,axiom,![A_27a, A_27b]: ![X0_2E0]: (s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E1(s(tyop_2Efinite__map_2Efmap(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Eoption_2Eoption(A_27a))),X0_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Eoption_2Eoption(A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Efinite__map_2EFDOM_2E0),s(tyop_2Efinite__map_2Efmap(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Eoption_2Eoption(A_27a))),X0_2E0))))).
fof(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27b,axiom,![A_27b]: ![X0_2E0, X1_2E0]: (s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(A_27b,X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))))).
fof(fmaptreeTheory_2Ewf__strongind,axiom,![A_27a, A_27b]: ![V0wf_27_2E0]: (![V1a_2E0, V2fm_2E0]: (![V3k_2E0]: (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,V3k_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E1(s(tyop_2Efinite__map_2Efmap(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Eoption_2Eoption(A_27a))),V2fm_2E0)))))) => (p(s(tyop_2Emin_2Ebool,c_2Efmaptree_2Ewf_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Eoption_2Eoption(A_27a)),c_2Efinite__map_2EFAPPLY_2E2(s(tyop_2Efinite__map_2Efmap(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Eoption_2Eoption(A_27a))),V2fm_2E0),s(A_27b,V3k_2E0)))))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),V0wf_27_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Eoption_2Eoption(A_27a)),c_2Efinite__map_2EFAPPLY_2E2(s(tyop_2Efinite__map_2Efmap(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Eoption_2Eoption(A_27a))),V2fm_2E0),s(A_27b,V3k_2E0)))))))) => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),V0wf_27_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Eoption_2Eoption(A_27a)),c_2Efmaptree_2Econstruct_2E2(s(A_27a,V1a_2E0),s(tyop_2Efinite__map_2Efmap(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Eoption_2Eoption(A_27a))),V2fm_2E0))))))) => ![V4a0_2E0]: (p(s(tyop_2Emin_2Ebool,c_2Efmaptree_2Ewf_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Eoption_2Eoption(A_27a)),V4a0_2E0)))) => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),V0wf_27_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Eoption_2Eoption(A_27a)),V4a0_2E0))))))).
