proposition: Lemma add0 x : 0 + x == x.
proof: Proof. split=> [a /open[b ltxb ltba] | a [b b_gt0] ltxab]. by exists (a - b)%R; [rewrite ltcE subr_gt0 | rewrite opprD opprK addNKr]. by apply: ltc_trans ltxab _; rewrite gtr_addl oppr_lt0. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq order) mathcomp(ssralg ssrnum ssrint rat) fourcolor(real) Coq(Setoid Morphisms)