[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, 2 insertions, 2 deletions

diff --git a/plugins/extraction/extract_env.ml b/plugins/extraction/extract_env.ml
index c5439ffaf6..4cd34100bc 100644
--- a/plugins/extraction/extract_env.ml
+++ b/plugins/extraction/extract_env.ml
@@ -752,13 +752,13 @@ let extract_and_compile l =
 (* Show the extraction of the current ongoing proof *)
 let show_extraction ~pstate =
   init ~inner:true false false;
-  let prf = Proof_global.give_me_the_proof pstate in
+  let prf = Proof_global.get_proof pstate in
   let sigma, env = Pfedit.get_current_context pstate in
   let trms = Proof.partial_proof prf in
   let extr_term t =
     let ast, ty = extract_constr env sigma t in
     let mp = Lib.current_mp () in
-    let l = Label.of_id (Proof_global.get_current_proof_name pstate) in
+    let l = Label.of_id (Proof_global.get_proof_name pstate) in
     let fake_ref = ConstRef (Constant.make2 mp l) in
     let decl = Dterm (fake_ref, ast, ty) in
     print_one_decl [] mp decl