fact: Axiom thm_ARITH_SUB : (forall m : nat, forall n : nat, (Nat.sub (NUMERAL m) (NUMERAL n)) = (NUMERAL (Nat.sub m n))) /\ (((Nat.sub 0 0) = 0) /\ ((forall n : nat, (Nat.sub 0 (BIT0 n)) = 0) /\ ((forall n : nat, (Nat.sub 0 (BIT1 n)) = 0) /\ ((forall n : nat, (Nat.sub (BIT0 n) 0) = (BIT0 n)) /\ ((forall n : nat, (Nat.sub (BIT1 n) 0) = (BIT1 n)) /\ ((forall m : nat, forall n : nat, (Nat.sub (BIT0 m) (BIT0 n)) = (BIT0 (Nat.sub m n))) /\ ((forall m : nat, forall n : nat, (Nat.sub (BIT0 m) (BIT1 n)) = (Nat.pred (BIT0 (Nat.sub m n)))) /\ ((forall m : nat, forall n : nat, (Nat.sub (BIT1 m) (BIT0 n)) = (@COND nat (Peano.le n m) (BIT1 (Nat.sub m n)) 0)) /\ (forall m : nat, forall n : nat, (Nat.sub (BIT1 m) (BIT1 n)) = (BIT0 (Nat.sub m n))))))))))).
imports: coq theory_hol types terms axioms