induction c.
intros.
assert (a = b) by intuition.
subst. auto.
intros.
assert (a >= (S b)) by omega.
assert (c = a - (S b)) by omega.
eapply ge_trans.
apply (IHc a (S b) pfa (s_nat_nz pfb)).
apply H1.
apply H2.
apply lognat_ge_monotonic_b.
Qed.

(* Specifications: *)
Lemma lognat_ge_monotonic : forall (a b : nat)(pfa : a <> 0)(pfb : b <> 0),
a >= b -> (lognat pfa) >= (lognat pfb).