src/Pure/proofterm.ML

--- a/src/Pure/proofterm.ML	Mon Dec 04 10:53:32 2023 +0100
+++ b/src/Pure/proofterm.ML	Mon Dec 04 12:10:39 2023 +0100
@@ -132,7 +132,6 @@
   val assumption_proof: term list -> term -> int -> proof -> proof
   val bicompose_proof: bool -> term list -> term list -> term option -> term list ->
     int -> int -> proof -> proof -> proof
-  val equality_axms: (string * term) list
   val reflexive_axm: proof
   val symmetric_axm: proof
   val transitive_axm: proof
@@ -1286,34 +1285,13 @@
 
 (** axioms for equality **)
 
-val aT = TFree ("'a", []);
-val bT = TFree ("'b", []);
-val x = Free ("x", aT);
-val y = Free ("y", aT);
-val z = Free ("z", aT);
-val A = Free ("A", propT);
-val B = Free ("B", propT);
-val f = Free ("f", aT --> bT);
-val g = Free ("g", aT --> bT);
-
-val equality_axms =
- [("reflexive", Logic.mk_equals (x, x)),
-  ("symmetric", Logic.mk_implies (Logic.mk_equals (x, y), Logic.mk_equals (y, x))),
-  ("transitive",
-    Logic.list_implies ([Logic.mk_equals (x, y), Logic.mk_equals (y, z)], Logic.mk_equals (x, z))),
-  ("equal_intr",
-    Logic.list_implies ([Logic.mk_implies (A, B), Logic.mk_implies (B, A)], Logic.mk_equals (A, B))),
-  ("equal_elim", Logic.list_implies ([Logic.mk_equals (A, B), A], B)),
-  ("abstract_rule",
-    Logic.mk_implies
-      (Logic.all x (Logic.mk_equals (f $ x, g $ x)),
-        Logic.mk_equals (lambda x (f $ x), lambda x (g $ x)))),
-  ("combination", Logic.list_implies
-    ([Logic.mk_equals (f, g), Logic.mk_equals (x, y)], Logic.mk_equals (f $ x, g $ y)))];
-
 val [reflexive_axm, symmetric_axm, transitive_axm, equal_intr_axm,
   equal_elim_axm, abstract_rule_axm, combination_axm] =
-    map (fn (s, t) => PAxm ("Pure." ^ s, Logic.varify_global t, NONE)) equality_axms;
+    Theory.equality_axioms |> map (fn (b, t) =>
+      let
+        val a = Sign.full_name (Sign.local_path (Context.the_global_context ())) b;
+        val A = Logic.varify_global t;
+      in PAxm (a, A, NONE) end);
 
 val reflexive_proof = reflexive_axm % NONE;