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 leqif_add_dist n1 n2 n3 :
`|n1 - n3| <= `|n1 - n2| + `|n2 - n3|
?= iff (n1 <= n2 <= n3) || (n3 <= n2 <= n1).