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diff --git a/backend/InterfGraphProperties.v b/backend/InterfGraphProperties.v
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+Require Import InterfGraph.
+Require Import Coloring.
+
+Lemma set_reg_reg_diff_ext : forall x f live live0,
+SetRegReg.In x (interf_reg_reg (interf_graph f live live0)) -> fst x <> snd x.
+
+Proof.
+Admitted.
+\ No newline at end of file