# 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()))
