right; intro; apply n; inversion H; subst; auto.
Defined.
+(* a WeakCoerVar just wraps a CoreVar and tags it with the pair of types amongst which it coerces *)
+Inductive WeakCoerVar := weakCoerVar : CoreVar -> Kind -> WeakType -> WeakType -> WeakCoerVar.
+
+Inductive WeakCoercion : Type :=
+| WCoVar : WeakCoerVar -> WeakCoercion (* g *)
+| WCoType : WeakType -> WeakCoercion (* τ *)
+| WCoApp : WeakCoercion -> WeakCoercion -> WeakCoercion (* γ γ *)
+| WCoAppT : WeakCoercion -> WeakType -> WeakCoercion (* γ@v *)
+| WCoAll : Kind -> (WeakTypeVar -> WeakCoercion) -> WeakCoercion (* ∀a:κ.γ *)
+| WCoSym : WeakCoercion -> WeakCoercion (* sym *)
+| WCoComp : WeakCoercion -> WeakCoercion -> WeakCoercion (* ◯ *)
+| WCoLeft : WeakCoercion -> WeakCoercion (* left *)
+| WCoRight : WeakCoercion -> WeakCoercion (* right *)
+| WCoUnsafe : WeakType -> WeakType -> WeakCoercion (* unsafe *)
+(*| WCoCFApp : ∀ n, CoFunConst n -> vec WeakCoercion n -> WeakCoercion (* C γⁿ *)*)
+(*| WCoTFApp : ∀ n, TyFunConst n -> vec WeakCoercion n -> WeakCoercion (* S_n γⁿ *)*)
+.
+
+Variable Prelude_error : forall {A}, string -> A. Extract Inlined Constant Prelude_error => "Prelude.error".
+Fixpoint weakCoercionTypes (wc:WeakCoercion) : WeakType * WeakType :=
+match wc with
+| WCoVar (weakCoerVar _ _ t1 t2) => (t1,t2)
+| WCoType t => Prelude_error "FIXME WCoType"
+| WCoApp c1 c2 => Prelude_error "FIXME WCoApp"
+| WCoAppT c t => Prelude_error "FIXME WCoAppT"
+| WCoAll k f => Prelude_error "FIXME WCoAll"
+| WCoSym c => let (t2,t1) := weakCoercionTypes c in (t1,t2)
+| WCoComp c1 c2 => Prelude_error "FIXME WCoComp"
+| WCoLeft c => Prelude_error "FIXME WCoLeft"
+| WCoRight c => Prelude_error "FIXME WCoRight"
+| WCoUnsafe t1 t2 => (t1,t2)
+end.
+
(* TO DO: write a proper EqDecidable instance for WeakType and then move the rest of this into HaskWeakToCore *)
Variable ModalBoxTyCon : TyCon. Extract Inlined Constant ModalBoxTyCon => "TysWiredIn.hetMetCodeTypeTyCon".
Variable ArrowTyCon : TyCon. Extract Constant ArrowTyCon => "Type.funTyCon".