∀ p, leibniz (filter_nat_type div_aux_body p) (div_aux p)

Theorem sym_eq_div_aux : forall (p:nat.nat), leibniz.leibniz (nat.nat -> nat.nat -> nat.nat) (nat.filter_nat_type (nat.nat -> nat.nat -> nat.nat) div_aux_body p) (div_aux p).

theorem sym_eq_div_aux : \forall (p:nat). (leibniz) (nat -> nat -> nat) ((filter_nat_type) (nat -> nat -> nat) (div_aux_body) p) ((div_aux) p).

theorem sym_eq_div_aux : forall (p:nat.nat) , (((leibniz.leibniz) ((nat.nat) -> (nat.nat) -> nat.nat)) ((((nat.filter_nat_type) ((nat.nat) -> (nat.nat) -> nat.nat)) ((div_mod.div_aux_body) )) (p))) (((div_mod.div_aux) ) (p)).

sym_eq_div_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]]](nat_sttfa_th.filter_nat_type[[nat_sttfa_th.sttfa_nat -> [nat_sttfa_th.sttfa_nat -> nat_sttfa_th.sttfa_nat]]](div_mod_sttfa.div_aux_body)(p))(div_mod_sttfa.div_aux(p)))

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