Using is_conv rather than eq_constr to find `nat` or `Z` in omega.

Moving at the same to a passing "env sigma" style rather than passing
"gl". Not that it is strictly necessary, but since we had to move
functions taking only a "sigma" to functions taking also a "env", we
eventually adopted the "env sigma" style. (The "gl" style would have
been as good.)

This answers wish #4717.

2 files changed, 35 insertions, 19 deletions

diff --git a/test-suite/bugs/closed/4717.v b/test-suite/bugs/closed/4717.v
new file mode 100644
index 0000000000..4562ed1f1a
--- /dev/null
+++ b/test-suite/bugs/closed/4717.v
@@ -0,0 +1,35 @@
+(* Omega being smarter on recognizing nat and Z *)
+
+Require Import Omega.
+
+Definition nat' := nat.
+
+Theorem le_not_eq_lt : forall (n m:nat),
+    n <= m ->
+    n <> m :> nat' ->
+    n < m.
+Proof.
+  intros.
+  omega.
+Qed.
+
+Goal forall (x n : nat'), x = x + n - n.
+Proof.
+  intros.
+  omega.
+Qed.
+
+Require Import ZArith.
+
+Open Scope Z_scope.
+
+Definition Z' := Z.
+
+Theorem Zle_not_eq_lt : forall n m,
+    n <= m ->
+    n <> m :> Z' ->
+    n < m.
+Proof.
+  intros.
+  omega.
+Qed.
diff --git a/test-suite/bugs/opened/4717.v b/test-suite/bugs/opened/4717.v
deleted file mode 100644
index 9ad4746723..0000000000
--- a/test-suite/bugs/opened/4717.v
+++ /dev/null
@@ -1,19 +0,0 @@
-(*See below. They sometimes work, and sometimes do not. Is this a bug?*)
-
-Require Import Omega Psatz.
-
-Definition foo := nat.
-
-Goal forall (n : foo), 0 = n - n.
-Proof. intros. omega. (* works *) Qed.
-
-Goal forall (x n : foo), x = x + n - n.
-Proof.
-  intros.
-  Fail omega. (* Omega can't solve this system *)
-  Fail lia. (* Cannot find witness. *)
-  unfold foo in *.
-  omega. (* works *)
-Qed.
-
-(* Guillaume Melquiond: What matters is the equality. In the first case, it is @eq nat. In the second case, it is @eq foo. The same issue exists for ring and field. So it is not a bug, but it is worth fixing.*)