Library Coq.Arith.Factorial
Require Import PeanoNat Plus Mult Lt.
Local Open Scope nat_scope.
Factorial
Fixpoint fact (n:nat) : nat :=
match n with
| O => 1
| S n => S n * fact n
end.
Lemma lt_O_fact n : 0 < fact n.
Lemma fact_neq_0 n : fact n <> 0.
Lemma fact_le n m : n <= m -> fact n <= fact m.