Commit 1a3f06a6 authored by Ralf Jung's avatar Ralf Jung

prelude.collections: add lemma to prove non-emptiness

parent 0da9298e
......@@ -280,6 +280,8 @@ Section collection.
intros X1 X2 HX Y1 Y2 HY; apply elem_of_equiv; intros x.
by rewrite !elem_of_difference, HX, HY.
Qed.
Lemma non_empty_inhabited x X : x X X .
Proof. solve_elem_of. Qed.
Lemma intersection_singletons x : ({[x]} : C) {[x]} {[x]}.
Proof. solve_elem_of. Qed.
Lemma difference_twice X Y : (X Y) Y X Y.
......
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