// This prints the left floatting menu

Theoremnat.minus_minus

Statement

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

Main Dependencies
Theory

Statement

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

Statement

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

Statement

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

Statement

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

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