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+Require Import SMTCoq.
+
+Parameter g : Z -> Z.
+
+Axiom g_2_linear : forall x, Zeq_bool (g (x + 1)) ((g x) + 2).
+
+Lemma apply_lemma_multiple :
+ forall x y, Zeq_bool (g (x + y)) ((g x) + y * 2).
+
+Proof.
+ verit g_2_linear.