Univs/(e)auto: fix bug #4450 polymorphic exact hints

The exact and e_exact tactics were not registering the universes and
constraints of the hint correctly. Now using the same connect_hint_clenv
as unify_resolve, they do. Also correct the implementation of
prepare_hint to normalize the universes of the hint before abstracting
its undefined universes. They are going to be refreshed at each
application. This means that eauto using term can
use multiple different instantiations of the universes of term
if term introduces new universes. If we want just one instantiation
then the term should be abbreviated in the goal first.

1 files changed, 58 insertions, 0 deletions

diff --git a/test-suite/bugs/closed/4450.v b/test-suite/bugs/closed/4450.v
new file mode 100644
index 000000000..ecebaba81
--- /dev/null
+++ b/test-suite/bugs/closed/4450.v
@@ -0,0 +1,58 @@
+Polymorphic Axiom inhabited@{u} : Type@{u} -> Prop.
+
+Polymorphic Axiom unit@{u} : Type@{u}.
+Polymorphic Axiom tt@{u} : inhabited unit@{u}.
+
+Polymorphic Hint Resolve tt : the_lemmas.
+Set Printing All.
+Set Printing Universes.
+Goal inhabited unit.
+Proof.
+  eauto with the_lemmas.
+Qed.
+
+Universe u.
+Axiom f : Type@{u} -> Prop.
+Lemma fapp (X : Type) : f X -> False.
+Admitted.
+Polymorphic Axiom funi@{i} : f unit@{i}.
+
+Goal (forall U, f U) -> (*(f unit -> False) ->  *)False /\ False.
+  eauto using (fapp unit funi). (* The two fapp's have different universes *)
+Qed.
+
+Hint Resolve (fapp unit funi) : mylems.
+
+Goal (forall U, f U) -> (*(f unit -> False) ->  *)False /\ False.
+  eauto with mylems. (* Forces the two fapps at the same level *)
+Qed.
+
+Goal (forall U, f U) -> (f unit -> False) -> False /\ False.
+  eauto. (* Forces the two fapps at the same level *)
+Qed.
+
+Polymorphic Definition MyType@{i} := Type@{i}.
+Universes l m n.
+Constraint l < m.
+Polymorphic Axiom maketype@{i} : MyType@{i}.
+
+Goal MyType@{l}.
+Proof.
+  Fail solve [ eauto using maketype@{m} ].
+  eauto using maketype.
+  Undo.
+  eauto using maketype@{n}.
+Qed.
+
+Axiom foo : forall (A : Type), list A.
+Polymorphic Axiom foop@{i} : forall (A : Type@{i}), list A.
+
+Universe x y.
+Goal list Type@{x}.
+Proof.
+  eauto using (foo Type). (* Refreshes the term *)
+  Undo.
+  eauto using foo. Show Universes.
+  Undo.
+  eauto using foop. Show Proof. Show Universes.
+Qed.
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