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Verified Commit 7453c90b authored by Lennard Gäher's avatar Lennard Gäher
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1 merge request!562Add lower bound lemma for finite sets
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...@@ -365,6 +365,7 @@ Lemma minimal_exists_elem_of_L R `{!LeibnizEquiv C, !Transitive R, ...@@ -365,6 +365,7 @@ Lemma minimal_exists_elem_of_L R `{!LeibnizEquiv C, !Transitive R,
x y, Decision (R x y)} (X : C) : x y, Decision (R x y)} (X : C) :
X x, x X minimal R x X. X x, x X minimal R x X.
Proof. unfold_leibniz. apply (minimal_exists_elem_of R). Qed. Proof. unfold_leibniz. apply (minimal_exists_elem_of R). Qed.
Lemma minimal_exists R `{!Transitive R, Lemma minimal_exists R `{!Transitive R,
x y, Decision (R x y)} `{!Inhabited A} (X : C) : x y, Decision (R x y)} `{!Inhabited A} (X : C) :
x, minimal R x X. x, minimal R x X.
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