proposition: Lemma RInt_gen_ext {Fa Fb : (R -> Prop) -> Prop} {FFa : ProperFilter Fa} {FFb : ProperFilter Fb} (f g : R -> V) : filter_prod Fa Fb (fun ab => forall x, Rmin (fst ab) (snd ab) < x < Rmax (fst ab) (snd ab) -> f x = g x) -> ex_RInt_gen f Fa Fb -> RInt_gen f Fa Fb = RInt_gen g Fa Fb.
proof: Proof. move => Heq [I HI]. rewrite (is_RInt_gen_unique f I HI); symmetry. apply is_RInt_gen_unique. by apply: is_RInt_gen_ext; first exact: Heq. Qed.
imports: Coq(Reals ssreflect) Rbar Hierarchy RInt Lim_seq Continuity Derive Rcomplements RInt_analysis