proposition: Lemma itercf_ind : (forall a x, C a x -> F a x a x) -> Transitive Fc -> (forall a x b y, R a x b y -> C a x -> C b y /\ F a x b y) -> forall a x b y, iterc R a x b y -> C a x -> F a x b y.
proof: Proof. move=>H1 H2 H3 a x b y; apply: (@iterf_ind _ Rc Cc Fc)=>//. - by case=>a' x'; apply: H1. by case=>a' x' [b' y']; apply: H3. Qed.
imports: Coq(ssreflect ssrbool ssrfun Setoid) mathcomp(ssrnat seq eqtype) pcm(options)