proposition: Lemma continuous_diff f g x: realp x -> continuous_at f x -> continuous_at g x -> continuous_at (fun z => f z -r g z) x.
proof: Proof. move => xr pa pb. apply:(continuous_sum xr pa); apply: (continuous_comp pb). apply: continuous_opp; apply:(continuous_real xr pb). Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)