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diff --git a/spartan/core/equality.ML b/spartan/core/equality.ML
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--- a/spartan/core/equality.ML
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@@ -1,90 +0,0 @@
-(*  Title:      equality.ML
-    Author:     Joshua Chen
-
-Equality reasoning with identity types.
-*)
-
-structure Equality:
-sig
-
-val dest_Id: term -> term * term * term
-
-val push_hyp_tac: term * term -> Proof.context -> int -> tactic
-val induction_tac: term -> term -> term -> term -> Proof.context -> tactic
-val equality_context_tac: Facts.ref -> Proof.context -> context_tactic
-
-end = struct
-
-fun dest_Id tm = case tm of
-    Const (\<^const_name>\<open>Id\<close>, _) $ A $ x $ y => (A, x, y)
-  | _ => error "dest_Id"
-
-(*Context assumptions that have already been pushed into the type family*)
-structure Inserts = Proof_Data (
-  type T = term Item_Net.T
-  val init = K (Item_Net.init Term.aconv_untyped single)
-)
-
-fun push_hyp_tac (t, _) =
-  Subgoal.FOCUS_PARAMS (fn {context = ctxt, concl, ...} =>
-    let
-      val (_, C) = Lib.dest_typing (Thm.term_of concl)
-      val B = Thm.cterm_of ctxt (Lib.lambda_var t C)
-      val a = Thm.cterm_of ctxt t
-      (*The resolvent is PiE[where ?B=B and ?a=a]*)
-      val resolvent =
-        Drule.infer_instantiate' ctxt [NONE, NONE, SOME B, SOME a] @{thm PiE}
-    in
-      HEADGOAL (resolve_tac ctxt [resolvent])
-      THEN SOMEGOAL (known_tac ctxt)
-    end)
-
-fun induction_tac p A x y ctxt =
-  let
-    val [p, A, x, y] = map (Thm.cterm_of ctxt) [p, A, x, y]
-  in
-    HEADGOAL (resolve_tac ctxt
-      [Drule.infer_instantiate' ctxt [SOME p, SOME A, SOME x, SOME y] @{thm IdE}])
-  end
-
-val side_conds_tac = TRY oo typechk_tac
-
-fun equality_context_tac fact ctxt =
-  let
-    val eq_th = Proof_Context.get_fact_single ctxt fact
-    val (p, (A, x, y)) = (Lib.dest_typing ##> dest_Id) (Thm.prop_of eq_th)
-
-    val hyps =
-      Facts.props (Proof_Context.facts_of ctxt)
-      |> filter (fn (th, _) => Lib.is_typing (Thm.prop_of th))
-      |> map (Lib.dest_typing o Thm.prop_of o fst)
-      |> filter_out (fn (t, _) =>
-          Term.aconv (t, p) orelse Item_Net.member (Inserts.get ctxt) t)
-      |> map (fn (t, T) => ((t, T), Lib.subterm_count_distinct [p, x, y] T))
-      |> filter (fn (_, i) => i > 0)
-      (*`t1: T1` comes before `t2: T2` if T1 contains t2 as subterm.
-        If they are incomparable, then order by decreasing
-        `subterm_count [p, x, y] T`*)
-      |> sort (fn (((t1, _), i), ((_, T2), j)) =>
-          Lib.cond_order (Lib.subterm_order T2 t1) (int_ord (j, i)))
-      |> map #1
-
-    val record_inserts =
-      Inserts.map (fold (fn (t, _) => fn net => Item_Net.update t net) hyps)
-
-    val tac =
-      fold (fn hyp => fn tac => tac THEN HEADGOAL (push_hyp_tac hyp ctxt))
-        hyps all_tac
-      THEN (
-        induction_tac p A x y ctxt
-        THEN RANGE (replicate 3 (typechk_tac ctxt) @ [side_conds_tac ctxt]) 1
-      )
-      THEN (
-        REPEAT_DETERM_N (length hyps) (SOMEGOAL (resolve_tac ctxt @{thms PiI}))
-        THEN ALLGOALS (side_conds_tac ctxt)
-      )
-  in
-    fn (ctxt, st) => Context_Tactic.TACTIC_CONTEXT (record_inserts ctxt) (tac st)
-  end
-
-end