∀ p, leibniz (gcd_aux p) (filter_nat_type gcd_aux_body p)

Theorem eq_gcd_aux : forall (p:nat.nat), leibniz.leibniz (nat.nat -> nat.nat -> nat.nat) (gcd_aux p) (nat.filter_nat_type (nat.nat -> nat.nat -> nat.nat) gcd_aux_body p).

theorem eq_gcd_aux : \forall (p:nat). (leibniz) (nat -> nat -> nat) ((gcd_aux) p) ((filter_nat_type) (nat -> nat -> nat) (gcd_aux_body) p).

theorem eq_gcd_aux : forall (p:nat.nat) , (((leibniz.leibniz) ((nat.nat) -> (nat.nat) -> nat.nat)) (((gcd.gcd_aux) ) (p))) ((((nat.filter_nat_type) ((nat.nat) -> (nat.nat) -> nat.nat)) ((gcd.gcd_aux_body) )) (p)).

eq_gcd_aux : LEMMA (FORALL(p:nat_sttfa_th.sttfa_nat):leibniz_sttfa_th.leibniz[[nat_sttfa_th.sttfa_nat -> [nat_sttfa_th.sttfa_nat -> nat_sttfa_th.sttfa_nat]]](gcd_sttfa.gcd_aux(p))(nat_sttfa_th.filter_nat_type[[nat_sttfa_th.sttfa_nat -> [nat_sttfa_th.sttfa_nat -> nat_sttfa_th.sttfa_nat]]](gcd_sttfa.gcd_aux_body)(p)))

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