∀ p, equal (mod_aux p) (filter_nat_type mod_aux_body p)

Axiom axiom_mod_aux : forall (p:nat.nat), connectives.equal (nat.nat -> nat.nat -> nat.nat) (mod_aux p) (nat.filter_nat_type (nat.nat -> nat.nat -> nat.nat) mod_aux_body p)

axiom axiom_mod_aux : \forall (p:nat). (equal) (nat -> nat -> nat) ((mod_aux) p) ((filter_nat_type) (nat -> nat -> nat) (mod_aux_body) p)

axiom axiom_mod_aux : forall (p:nat.nat) , (((connectives.equal) ((nat.nat) -> (nat.nat) -> nat.nat)) (((div_mod.mod_aux) ) (p))) ((((nat.filter_nat_type) ((nat.nat) -> (nat.nat) -> nat.nat)) ((div_mod.mod_aux_body) )) (p))

axiom_mod_aux : AXIOM (FORALL(p:nat_sttfa_th.sttfa_nat):connectives_sttfa_th.equal[[nat_sttfa_th.sttfa_nat -> [nat_sttfa_th.sttfa_nat -> nat_sttfa_th.sttfa_nat]]](div_mod_sttfa.mod_aux(p))(nat_sttfa_th.filter_nat_type[[nat_sttfa_th.sttfa_nat -> [nat_sttfa_th.sttfa_nat -> nat_sttfa_th.sttfa_nat]]](div_mod_sttfa.mod_aux_body)(p)))

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