# Copyright (C) 2013 Korei Klein <*****@*****.**> from calculus.enriched import constructors from lib import natural, library, common_vars, equivalence, function # A proof that forall n : N . S (S n) > n n = common_vars.n() a = common_vars.a() b = common_vars.b() claim = natural.Less(natural.zero, constructors.Apply( constructors.Apply(natural.zero, natural.S) , natural.S)) proof = natural.lib.beginProof().forwardFollow(lambda p: p.onPathFollow(lambda x: constructors.assume(x, claim))) proof = proof.forwardFollow(lambda p: p.onPathFollow(lambda x: x.forwardSimplify()))