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+Section test.
+Variable n:nat.
+Lemma foo: 0 <= n.
+Proof.
+(* declaring an Axiom during a proof makes it immediatly
+ usable, juste as a full Definition. *)
+Axiom bar : n = 1.
+rewrite bar.
+now apply le_S.
+Qed.
+
+Lemma foo' : 0 <= n.
+Proof.
+(* Declaring an Hypothesis during a proof is ok,
+ but this hypothesis won't be usable by the current proof(s),
+ only by later ones. *)
+Hypothesis bar' : n = 1.
+Fail rewrite bar'.
+Abort.
+
+Lemma foo'' : 0 <= n.
+Proof.
+rewrite bar'.
+now apply le_S.
+Qed.
+
+End test. \ No newline at end of file