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+Require Import Crypto.Compilers.Syntax.
+Require Import Crypto.Compilers.Wf.
+Require Import Crypto.Compilers.SmartMap.
+Require Import Crypto.Compilers.Relations.
+Require Import Crypto.Compilers.MapCastByDeBruijnInterp.
+Require Import Crypto.Compilers.Z.Syntax.
+Require Import Crypto.Compilers.Z.MapCastByDeBruijn.
+
+Section language.
+  Context {interp_base_type_bounds : base_type -> Type}
+          (interp_op_bounds : forall src dst, op src dst -> interp_flat_type interp_base_type_bounds src -> interp_flat_type interp_base_type_bounds dst)
+          (pick_typeb : forall t, interp_base_type_bounds t -> base_type).
+  Local Notation pick_type v := (SmartFlatTypeMap pick_typeb v).
+  Context (cast_op : forall t tR (opc : op t tR) args_bs,
+              op (pick_type args_bs) (pick_type (interp_op_bounds t tR opc args_bs)))
+          (cast_backb: forall t b, interp_base_type (pick_typeb t b) -> interp_base_type t).
+  Let cast_back : forall t b, interp_flat_type interp_base_type (pick_type b) -> interp_flat_type interp_base_type t
+    := fun t b => SmartFlatTypeMapUnInterp cast_backb.
+  Context (inboundsb : forall t, interp_base_type_bounds t -> interp_base_type t -> Prop).
+  Let inbounds : forall t, interp_flat_type interp_base_type_bounds t -> interp_flat_type interp_base_type t -> Prop
+    := fun t => interp_flat_type_rel_pointwise inboundsb (t:=t).
+  Context (interp_op_bounds_correct
+           : forall t tR opc bs
+                    (v : interp_flat_type interp_base_type t)
+                    (H : inbounds t bs v),
+              inbounds tR (interp_op_bounds t tR opc bs) (interp_op t tR opc v))
+          (pull_cast_back
+           : forall t tR opc bs
+                    (v : interp_flat_type interp_base_type (pick_type bs))
+                    (H : inbounds t bs (cast_back t bs v)),
+              interp_op t tR opc (cast_back t bs v)
+              =
+              cast_back _ _ (interp_op _ _ (cast_op _ _ opc bs) v)).
+
+  Local Notation MapCast
+    := (@MapCast interp_base_type_bounds interp_op_bounds pick_typeb cast_op).
+
+  Lemma MapCastCorrect
+        {t} (e : Expr base_type op t)
+        (Hwf : Wf e)
+        (input_bounds : interp_flat_type interp_base_type_bounds (domain t))
+    : forall {b} e' (He':MapCast e input_bounds = Some (existT _ b e'))
+             v v' (Hv : @inbounds _ input_bounds v /\ cast_back _ _ v' = v),
+      Interp interp_op_bounds e input_bounds = b
+      /\ @inbounds _ b (Interp interp_op e v)
+      /\ cast_back _ _ (Interp interp_op e' v') = (Interp interp_op e v).
+  Proof using Type*.
+    apply MapCastCorrect; auto using internal_base_type_dec_lb.
+  Qed.
+End language.