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finmap.v
@@ -1902,6 +1902,9 @@ apply/idP/idP => [subA|/andP [AB CA]]; last by rewrite -[A]fsetUid fsetUSS.
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by rewrite !(fsubset_trans _ subA).
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Qed.
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+Lemma fsubU1set x A B : (x |` A `<=` B) = (x \in B) && (A `<=` B).
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+Proof. by rewrite fsubUset fsub1set. Qed.
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+
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Lemma fsubUsetP A B C : reflect (A `<=` C /\ B `<=` C) (A `|` B `<=` C).
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Proof. by rewrite fsubUset; exact: andP. Qed.
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