a>asize_symbolaVar_symbolV0c0ItF
VC for size_positive_lemma_symbol
a>asize_symbolV0c0F
a=arename_symbolarename_symbolV4V2V3arename_symbolV4arcomposeV2V3ItLaVar_symbolV1F
VC for renaming_composition_lemma_symbol
a=arename_symbolarename_symbolV1V2V3arename_symbolV1arcomposeV2V3F
a=arename_symbolV5aidentityV5ItLaVar_symbolV4F
VC for renaming_identity_lemma_symbol
a=arename_symbolV4aidentityV4F
a=a@arename_subst_symbolV5V6V7arename_symbola@V5V7V6F
a=arename_subst_symbolV8arcomposeV9V10arename_subst_symbolarename_subst_symbolV8V9V10AaextensionalEqualarename_subst_symbolV8arcomposeV9V10arename_subst_symbolarename_subst_symbolV8V9V10F
VC for associativity_subst_rename_rename_lemma_symbol
a=arename_subst_symbolV8arcomposeV9V10arename_subst_symbolarename_subst_symbolV8V9V10F
a=arcomposeV11arename_subst_symbolV12V13arename_subst_symbolarcomposeV11V12V13AaextensionalEqualarcomposeV11arename_subst_symbolV12V13arename_subst_symbolarcomposeV11V12V13F
VC for associativity_rename_subst_rename_lemma_symbol
a=arcomposeV11arename_subst_symbolV12V13arename_subst_symbolarcomposeV11V12V13F
a=arename_subst_symbolV14aidentityV14AaextensionalEqualarename_subst_symbolV14aidentityV14F
VC for right_rename_subst_by_identity_lemma_symbol
a=arename_subst_symbolV14aidentityV14F
a=aolifts_symbolarcomposeV15V16arcomposeaoliftV15aolifts_symbolV16AaextensionalEqualaolifts_symbolarcomposeV15V16arcomposeaoliftV15aolifts_symbolV16ACa=aevalaolifts_symbolarcomposeV15V16V17aevalarcomposeaoliftV15aolifts_symbolV16V17aNonea=aevalarename_subst_symbolaolifts_symbolV16aidentitya@arcomposeV15asomeV18aevalarcomposeaoliftV15aolifts_symbolV16V17Aa=aevalarcomposeV15arename_subst_symbolV16asomeV18aevalarename_subst_symbolaolifts_symbolV16aidentitya@arcomposeV15asomeV18Aa=aevalaolifts_symbolarcomposeV15V16V17aevalarcomposeV15arename_subst_symbolV16asomeV18aSomeVV17FF
VC for olifts_composition_lemma_rename_subst_symbol
a=aolifts_symbolarcomposeV15V16arcomposeaoliftV15aolifts_symbolV16F
a=aolifts_symbolarename_subst_symbolV17V18arename_subst_symbolaolifts_symbolV17aoliftV18AaextensionalEqualaolifts_symbolarename_subst_symbolV17V18arename_subst_symbolaolifts_symbolV17aoliftV18ACa=aevalaolifts_symbolarename_subst_symbolV17V18V19aevalarename_subst_symbolaolifts_symbolV17aoliftV18V19aNonea=arename_symbolarename_symbola@V17V20asomeaoliftV18aevalarename_subst_symbolaolifts_symbolV17aoliftV18V19Aa=aevalarename_subst_symbolV17arcomposeV18asomeV20arename_symbolarename_symbola@V17V20asomeaoliftV18Aa=aevalaolifts_symbolarename_subst_symbolV17V18V19aevalarename_subst_symbolV17arcomposeV18asomeV20aSomeVV19FF
VC for olifts_composition_lemma_subst_rename_symbol
a=aolifts_symbolarename_subst_symbolV17V18arename_subst_symbolaolifts_symbolV17aoliftV18F
a=asubst_symbolarename_symbolV22V20V21asubst_symbolV22arcomposeV20V21ItLaVar_symbolV19F
VC for rename_then_subst_composition_lemma_symbol
a=asubst_symbolarename_symbolV19V20V21asubst_symbolV19arcomposeV20V21F
a=arename_symbolasubst_symbolV25V23V24asubst_symbolV25arename_subst_symbolV23V24ItLaVar_symbolV22F
VC for subst_then_rename_composition_lemma_symbol
a=arename_symbolasubst_symbolV22V23V24asubst_symbolV22arename_subst_symbolV23V24F
a=a@asubst_compose_symbolV25V26V27asubst_symbola@V25V27V26F
a=arcomposeV28asubst_compose_symbolV29V30asubst_compose_symbolarcomposeV28V29V30AaextensionalEqualarcomposeV28asubst_compose_symbolV29V30asubst_compose_symbolarcomposeV28V29V30F
VC for associativity_rename_subst_subst_lemma_symbol
a=arcomposeV28asubst_compose_symbolV29V30asubst_compose_symbolarcomposeV28V29V30F
a=asubst_compose_symbolV31arcomposeV32V33asubst_compose_symbolarename_subst_symbolV31V32V33AaextensionalEqualasubst_compose_symbolV31arcomposeV32V33asubst_compose_symbolarename_subst_symbolV31V32V33F
VC for associativity_subst_rename_subst_lemma_symbol
a=asubst_compose_symbolV31arcomposeV32V33asubst_compose_symbolarename_subst_symbolV31V32V33F
a=asubst_compose_symbolV34arename_subst_symbolV35V36arename_subst_symbolasubst_compose_symbolV34V35V36AaextensionalEqualasubst_compose_symbolV34arename_subst_symbolV35V36arename_subst_symbolasubst_compose_symbolV34V35V36F
VC for associativity_subst_subst_rename_lemma_symbol
a=asubst_compose_symbolV34arename_subst_symbolV35V36arename_subst_symbolasubst_compose_symbolV34V35V36F
a=aolifts_symbolasubst_compose_symbolV37V38asubst_compose_symbolaolifts_symbolV37aolifts_symbolV38AaextensionalEqualaolifts_symbolasubst_compose_symbolV37V38asubst_compose_symbolaolifts_symbolV37aolifts_symbolV38ACa=aevalaolifts_symbolasubst_compose_symbolV37V38V39aevalasubst_compose_symbolaolifts_symbolV37aolifts_symbolV38V39aNonea=asubst_symbolarename_symbola@V37V40asomearename_subst_symbolaolifts_symbolV38aidentityaevalasubst_compose_symbolaolifts_symbolV37aolifts_symbolV38V39Aa=aevalasubst_compose_symbolV37arename_subst_symbolV38asomeV40asubst_symbolarename_symbola@V37V40asomearename_subst_symbolaolifts_symbolV38aidentityAa=aevalaolifts_symbolasubst_compose_symbolV37V38V39aevalasubst_compose_symbolV37arename_subst_symbolV38asomeV40aSomeVV39FF
VC for olifts_composition_lemma_subst_subst_symbol
a=aolifts_symbolasubst_compose_symbolV37V38asubst_compose_symbolaolifts_symbolV37aolifts_symbolV38F
a=asubst_symbolasubst_symbolV42V40V41asubst_symbolV42asubst_compose_symbolV40V41ItLaVar_symbolV39F
VC for subst_composition_lemma_symbol
a=asubst_symbolasubst_symbolV39V40V41asubst_symbolV39asubst_compose_symbolV40V41F
a=asubst_compose_symbolV42asubst_compose_symbolV43V44asubst_compose_symbolasubst_compose_symbolV42V43V44AaextensionalEqualasubst_compose_symbolV42asubst_compose_symbolV43V44asubst_compose_symbolasubst_compose_symbolV42V43V44F
VC for associativity_subst_subst_subst_lemma_symbol
a=asubst_compose_symbolV42asubst_compose_symbolV43V44asubst_compose_symbolasubst_compose_symbolV42V43V44F
a=aevalasubst_id_symbolV45aVar_symbolV45F
a=aolifts_symbolasubst_id_symbolasubst_id_symbolAaextensionalEqualaolifts_symbolasubst_id_symbolasubst_id_symbolACa=aevalaolifts_symbolasubst_id_symbolV46aevalasubst_id_symbolV46aNonea=aevalaolifts_symbolasubst_id_symbolV46aevalasubst_id_symbolV46aSomeVV46F
VC for olifts_identity_symbol
a=aolifts_symbolasubst_id_symbolasubst_id_symbol
a=arename_subst_symbolasubst_id_symbolV46asubst_of_rename_symbolV46AaextensionalEqualarename_subst_symbolasubst_id_symbolV46asubst_of_rename_symbolV46F
VC for left_rename_subst_identity_lemma_symbol
a=arename_subst_symbolasubst_id_symbolV46asubst_of_rename_symbolV46F
a=asubst_symbolV48asubst_id_symbolV48ItLaVar_symbolV47F
VC for subst_identity_lemma_symbol
a=asubst_symbolV47asubst_id_symbolV47F
a=asubst_compose_symbolasubst_id_symbolV48V48AaextensionalEqualasubst_compose_symbolasubst_id_symbolV48V48F
VC for left_subst_subst_identity_lemma_symbol
a=asubst_compose_symbolasubst_id_symbolV48V48F
a=asubst_compose_symbolV49asubst_id_symbolV49AaextensionalEqualasubst_compose_symbolV49asubst_id_symbolV49F
VC for right_subst_subst_by_identity_lemma_symbol
a=asubst_compose_symbolV49asubst_id_symbolV49F
a=asize_symbolarename_symbolV52V51asize_symbolV52ItLaVar_symbolV50F
VC for renaming_preserve_size_symbol
a=asize_symbolarename_symbolV50V51asize_symbolV50F
a=a@V54V56V52Aais_symbol_free_var_in_symbolV56V55Ia=V56V53FIais_symbol_free_var_in_symbolV52arename_symbolV55V54LaVar_symbolV53F
VC for rename_free_var_constructive_inversion_symbol_symbol
a=a@V54V57V52Aais_symbol_free_var_in_symbolV57V55EIa=a@V54V56V52Aais_symbol_free_var_in_symbolV56V55FAais_symbol_free_var_in_symbolV52arename_symbolV55V54Aa<asize_symbolV55a+c1asize_symbolV55Aa<=c0a+c1asize_symbolV55Iais_symbol_free_var_in_symbolV52arename_symbolV55V54LaVar_symbolV53F
VC for rename_free_var_inversion_symbol_symbol
a=a@V54V55V52Aais_symbol_free_var_in_symbolV55V53EIais_symbol_free_var_in_symbolV52arename_symbolV53V54F
ais_symbol_free_var_in_symbola@V58V56arename_symbolV59V58Iais_symbol_free_var_in_symbolV56V59ItLaVar_symbolV57F
VC for rename_free_var_propagation_symbol_symbol
ais_symbol_free_var_in_symbola@V58V56arename_symbolV57V58Iais_symbol_free_var_in_symbolV56V57F
ais_symbol_free_var_in_symbolV59a@V61V63Aais_symbol_free_var_in_symbolV63V62Ia=V63V60FIais_symbol_free_var_in_symbolV59asubst_symbolV62V61LaVar_symbolV60F
VC for subst_free_var_constructive_inversion_symbol_symbol
a<asize_symbolV62a+c1asize_symbolV62Aa<=c0a+c1asize_symbolV62Iais_symbol_free_var_in_symbolV59asubst_symbolV62V61LaVar_symbolV60F
variant decrease
ais_symbol_free_var_in_symbolV59asubst_symbolV62V61Iais_symbol_free_var_in_symbolV59asubst_symbolV62V61LaVar_symbolV60F
precondition
ais_symbol_free_var_in_symbolV59a@V61V64Aais_symbol_free_var_in_symbolV64V62EIais_symbol_free_var_in_symbolV59a@V61V63Aais_symbol_free_var_in_symbolV63V62FIais_symbol_free_var_in_symbolV59asubst_symbolV62V61LaVar_symbolV60F
postcondition
ais_symbol_free_var_in_symbolV59a@V61V64Aais_symbol_free_var_in_symbolV64V62EIais_symbol_free_var_in_symbolV59a@V61V63Aais_symbol_free_var_in_symbolV63V62FAais_symbol_free_var_in_symbolV59asubst_symbolV62V61Aa<asize_symbolV62a+c1asize_symbolV62Aa<=c0a+c1asize_symbolV62Iais_symbol_free_var_in_symbolV59asubst_symbolV62V61LaVar_symbolV60F
VC for subst_free_var_inversion_symbol_symbol
ais_symbol_free_var_in_symbolV59a@V61V62Aais_symbol_free_var_in_symbolV62V60EIais_symbol_free_var_in_symbolV59asubst_symbolV60V61F
ais_symbol_free_var_in_symbolV64asubst_symbolV67V66Iais_symbol_free_var_in_symbolV64a@V66V63Aais_symbol_free_var_in_symbolV63V67ItLaVar_symbolV65F
VC for subst_free_var_propagation_symbol_symbol_symbol
ais_symbol_free_var_in_symbolV64asubst_symbolV65V66Iais_symbol_free_var_in_symbolV64a@V66V63Aais_symbol_free_var_in_symbolV63V65F
a=asubst_symbolV70V68asubst_symbolV70V69ItIa=a@V68V71a@V69V71Iais_symbol_free_var_in_symbolV71V70FLaVar_symbolV67F
VC for free_var_equivalence_of_subst_symbol
a=asubst_symbolV67V68asubst_symbolV67V69Ia=a@V68V70a@V69V70Iais_symbol_free_var_in_symbolV70V67FF
a=arename_symbolV74V72arename_symbolV74V73Ia=asubst_symbolV74V76asubst_symbolV74V75Aa=a@V76V77a@V75V77Iais_symbol_free_var_in_symbolV77V74FLasubst_of_rename_symbolV72Lasubst_of_rename_symbolV73Ia=a@V72V78a@V73V78Iais_symbol_free_var_in_symbolV78V74FLaVar_symbolV71F
VC for free_var_equivalence_of_rename_symbol
a=arename_symbolV71V72arename_symbolV71V73Ia=a@V72V74a@V73V74Iais_symbol_free_var_in_symbolV74V71FF
a=a@V76V79a@V77V79Iais_symbol_free_var_in_symbolV79V78FItIa=asubst_symbolV78V76asubst_symbolV78V77LaVar_symbolV75F
VC for free_var_derive_equivalence_of_subst_symbol
a=a@V76V78a@V77V78Iais_symbol_free_var_in_symbolV78V75FIa=asubst_symbolV75V76asubst_symbolV75V77F
a=a@V80V85a@V81V85Iais_symbol_free_var_in_symbolV85V82FAa=a@V80V86a@V81V86Aa=a@V80V86a@V81V86Ia=a@asubst_of_rename_symbolV80V86a@asubst_of_rename_symbolV81V86FIa=a@V84V87a@V83V87Iais_symbol_free_var_in_symbolV87V82FAa=asubst_symbolV82V84asubst_symbolV82V83Lasubst_of_rename_symbolV80Lasubst_of_rename_symbolV81Ia=arename_symbolV82V80arename_symbolV82V81LaVar_symbolV79F
VC for free_var_derive_equivalence_of_rename_symbol

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