Omega: use "simpl" only on coefficents, not on atoms (fix #4132)

 Two issues in one:
  - some focused_simpl were called on the wrong locations
  - some focused_simpl were done on whole equations

 In the two cases, this could be bad if "simpl" goes too far
 with respect to what omega expects: later calls to "occurrence"
 might fail. This may happen for instance if an atom isn't a variable,
 but a let-in (b:=5:Z in the example).

1 files changed, 31 insertions, 0 deletions

diff --git a/test-suite/bugs/closed/4132.v b/test-suite/bugs/closed/4132.v
new file mode 100644
index 000000000..806ffb771
--- /dev/null
+++ b/test-suite/bugs/closed/4132.v
@@ -0,0 +1,31 @@
+
+Require Import ZArith Omega.
+Open Scope Z_scope.
+
+(** bug 4132: omega was using "simpl" either on whole equations, or on
+   delimited but wrong spots. This was leading to unexpected reductions
+   when one atom (here [b]) is an evaluable reference instead of a variable. *)
+
+Lemma foo
+  (x y x' zxy zxy' z : Z)
+  (b := 5)
+  (Ry : - b <= y < b)
+  (Bx : x' <= b)
+  (H : - zxy' <= zxy)
+  (H' : zxy' <= x') : - b <= zxy.
+Proof.
+omega. (* was: Uncaught exception Invalid_argument("index out of bounds"). *)
+Qed.
+
+Lemma foo2 x y (b := 5) (H1 : x <= y) (H2 : y <= b) : x <= b.
+omega. (* Pierre L: according to a comment of bug report #4132,
+          this might have triggered "index out of bounds" in the past,
+          but I never managed to reproduce that in any version,
+          even before my fix. *)
+Qed.
+
+Lemma foo3 x y (b := 0) (H1 : x <= y) (H2 : y <= b) : x <= b.
+omega. (* Pierre L: according to a comment of bug report #4132,
+          this might have triggered "Failure(occurence 2)" in the past,
+          but I never managed to reproduce that. *)
+Qed.