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+Require Import ssreflect ssrbool eqtype ssrnat.
+
+Lemma test x : (x == x) = (x + x.+1 == 2 * x + 1).
+case: (X in _ = X) / eqP => _.
+match goal with |- (x == x) = true => admit end.
+match goal with |- (x == x) = false => admit end.
+Qed.
+
+Lemma test1 x : (x == x) = (x + x.+1 == 2 * x + 1).
+elim: (x in RHS).
+match goal with |- (x == x) = _ => admit end.
+match goal with |- forall n, (x == x) = _ -> (x == x) = _ => admit end.
+Qed.
+