// This prints the left floatting menu

### Theoremnat.minus_to_plus

Statement

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

Main Dependencies
Theory

Statement

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

Statement

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

Statement

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

Statement

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

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