Section Multiplicative.
Variables (R S : ringType) (f : {rmorphism R -> S}).
Fact ler_wpeexpz2l x (x1 : 1 <= x) :
{in >= 0 &, {homo (exprz x) : x y / x <= y}}.
Fact ler_wneexpz2l x (x1 : 1 <= x) :
{in <= 0 &, {homo (exprz x) : x y / x <= y}}.

Lemma sgzX (n : nat) x : sgz (x ^+ n) = (sgz x) ^+ n.