∀ m n p, m ≤ n ⇒ ((n - m) + p) = ((n + p) - m)

Theorem plus_minus : forall (m:nat), forall (n:nat), forall (p:nat), (le m n) -> logic.eq (nat) (plus (minus n m) p) (minus (plus n p) m).

theorem plus_minus : \forall (m:nat). \forall (n:nat). \forall (p:nat). ((le) m n) -> (eq) (nat) ((plus) ((minus) n m) p) ((minus) ((plus) n p) m).

theorem plus_minus : forall (m:nat.nat) , forall (n:nat.nat) , forall (p:nat.nat) , ((((nat.le_) ) (m)) (n)) -> (((logic.eq_) (nat.nat)) ((((nat.plus) ) ((((nat.minus) ) (n)) (m))) (p))) ((((nat.minus) ) ((((nat.plus) ) (n)) (p))) (m)).

plus_minus : LEMMA (FORALL(m:nat_sttfa.sttfa_nat):(FORALL(n:nat_sttfa.sttfa_nat):(FORALL(p:nat_sttfa.sttfa_nat):(nat_sttfa.le(m)(n) => logic_sttfa_th.eq[nat_sttfa.sttfa_nat](nat_sttfa.plus(nat_sttfa.minus(n)(m))(p))(nat_sttfa.minus(nat_sttfa.plus(n)(p))(m))))))

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