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+From Coq Require Import ssreflect.
+
+Axiom subnn : forall n : nat, n - n = 0.
+Parameter G : (nat -> nat) -> nat -> nat.
+Axiom eq_G :
+ forall F1 F2 : nat -> nat,
+ (forall n : nat, F1 n = F2 n) ->
+ forall n : nat, G F1 n = G F2 n.
+
+Ltac show := match goal with [|-?g] => idtac g end.
+
+Lemma example_G (n : nat) : G (fun n => n - n) n >= 0.
+under eq_G => m do [show; rewrite subnn].
+show.
+Abort.
+
+Parameters (R Rbar : Set) (R0 : R) (Rbar0 : Rbar).
+Parameter Rbar_le : Rbar -> Rbar -> Prop.
+Parameter Lub_Rbar : (R -> Prop) -> Rbar.
+Parameter Lub_Rbar_eqset :
+ forall E1 E2 : R -> Prop,
+ (forall x : R, E1 x <-> E2 x) ->
+ Lub_Rbar E1 = Lub_Rbar E2.
+
+Lemma test_Lub_Rbar (E : R -> Prop) :
+ Rbar_le Rbar0 (Lub_Rbar (fun x => x = R0 \/ E x)).
+Proof.
+under Lub_Rbar_eqset => r do show.
+show.
+Abort.