set "baseuri" "cic:/matita/nat/sigma_and_pi".
+include "nat/factorial.ma".
include "nat/lt_arith.ma".
let rec sigma n f \def
apply H.intros.apply H1.
apply trans_lt ? n1.assumption.simplify.apply le_n.
qed.
+
+theorem eq_fact_pi: \forall n. n! = pi n S.
+intro.elim n.
+simplify.reflexivity.
+change with (S n1)*n1! = (S n1)*(pi n1 S).
+apply eq_f.assumption.
+qed.
\ No newline at end of file