[proof] Move proofs that have an associated constant to `Lemmas`

The main idea of this PR is to distinguish the types of "proof object"
`Proof_global.t` and the type of "proof object associated to a
constant, the new `Lemmas.t`.

This way, we can move the terminator setup to the higher layer in
`vernac`, which is the one that really knows about constants, paving
the way for further simplification and in particular for a unified
handling of constant saving by removal of the control inversion here.

Terminators are now internal to `Lemmas`, as it is the only part of
the code applying them.

As a consequence, proof nesting is now handled by `Lemmas`, and
`Proof_global.t` is just a single `Proof.t` plus some environmental
meta-data.

We are also enable considerable simplification in a future PR, as this
patch makes `Proof.t` and `Proof_global.t` essentially the same, so we
should expect to handle them under a unified interface.

1 files changed, 9 insertions, 9 deletions

diff --git a/vernac/classes.ml b/vernac/classes.ml
index ed207b52dd..b64af52b6e 100644
--- a/vernac/classes.ml
+++ b/vernac/classes.ml
@@ -378,11 +378,11 @@ let declare_instance_open sigma ?hook ~tac ~global ~poly id pri imps decl ids te
   let gls = List.rev (Evd.future_goals sigma) in
   let sigma = Evd.reset_future_goals sigma in
   let kind = Decl_kinds.(Global ImportDefaultBehavior, poly, DefinitionBody Instance) in
-  let pstate = Lemmas.start_proof id ~pl:decl kind sigma (EConstr.of_constr termtype)
+  let lemma = Lemmas.start_lemma id ~pl:decl kind sigma (EConstr.of_constr termtype)
       ~hook:(Lemmas.mk_hook
                (fun _ _ _ -> instance_hook pri global imps ?hook)) in
   (* spiwack: I don't know what to do with the status here. *)
-  let pstate =
+  let lemma =
     if not (Option.is_empty term) then
       let init_refine =
         Tacticals.New.tclTHENLIST [
@@ -391,18 +391,18 @@ let declare_instance_open sigma ?hook ~tac ~global ~poly id pri imps decl ids te
           Tactics.New.reduce_after_refine;
         ]
       in
-      let pstate, _ = Pfedit.by init_refine pstate in
-      pstate
+      let lemma, _ = Lemmas.by init_refine lemma in
+      lemma
     else
-      let pstate, _ = Pfedit.by (Tactics.auto_intros_tac ids) pstate in
-      pstate
+      let lemma, _ = Lemmas.by (Tactics.auto_intros_tac ids) lemma in
+      lemma
   in
   match tac with
   | Some tac ->
-    let pstate, _ = Pfedit.by tac pstate in
-    pstate
+    let lemma, _ = Lemmas.by tac lemma in
+    lemma
   | None ->
-    pstate
+    lemma
 
 let do_instance_subst_constructor_and_ty subst k u ctx =
   let subst =