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+(* (c) Copyright Microsoft Corporation and Inria. All rights reserved. *)
+Require Import ssreflect ssrbool ssrnat.
+
+Goal forall m n p, n <= p -> m <= n -> m <= p.
+by move=> m n p le_n_p /leq_trans; apply.
+Undo 1.
+by move=> m n p le_n_p /leq_trans /(_ le_n_p) le_m_p; exact: le_m_p.
+Undo 1.
+by move=> m n p le_n_p /leq_trans ->.
+Qed.
+
+Goal forall P Q X : Prop, Q -> (True -> X -> Q = P) -> X -> P.
+by move=> P Q X q V /V <-.
+Qed.
+
+Lemma test0: forall a b, a && a && b -> b.
+by move=> a b; repeat move=> /andP []; move=> *.
+Qed.
+
+Lemma test1 : forall a b, a && b -> b.
+by move=> a b /andP /andP /andP [] //.
+Qed.
+
+Lemma test2 : forall a b, a && b -> b.
+by move=> a b /andP /andP /(@andP a) [] //.
+Qed.
+
+Lemma test3 : forall a b, a && (b && b) -> b.
+by move=> a b /andP [_ /andP [_ //]].
+Qed.
+
+Lemma test4:  forall a b, a && b = b && a.
+by move=> a b; apply/andP/andP=> ?; apply/andP/andP/andP; rewrite andbC; apply/andP.
+Qed.
+
+Lemma test5:  forall C I A O, (True -> O) -> (O -> A) -> (True -> A -> I) -> (I -> C) -> C.
+by move=> c i a o O A I C; apply/C/I/A/O.
+Qed.
+
+Lemma test6:  forall A B, (A -> B) -> A -> B.
+move=> A B A_to_B a; move/A_to_B in a; exact: a.
+Qed.
+
+Lemma test7:  forall A B, (A -> B) -> A -> B.
+move=> A B A_to_B a; apply A_to_B in a; exact: a.
+Qed.
+
+Require Import ssrfun eqtype ssrnat div seq choice fintype finfun finset.
+
+Lemma test8 (T : finType) (A B : {set T}) x (Ax : x \in A) (_ : B = A) : x \in B.
+apply/subsetP: x Ax.
+by rewrite H subxx.
+Qed.
+
+
+