+ (* an "EGlobal" is any variable which is free in the expression which was passed to -fcoqpass (ie bound outside it) *)
+ | EGlobal: forall Γ Δ ξ (g:Global Γ) v lev, Expr Γ Δ ξ (g v) lev
+
+ | EVar : ∀ Γ Δ ξ ev, Expr Γ Δ ξ (unlev (ξ ev)) (getlev (ξ ev))
+ | ELit : ∀ Γ Δ ξ lit l, Expr Γ Δ ξ (literalType lit) l
+ | EApp : ∀ Γ Δ ξ t1 t2 l, Expr Γ Δ ξ (t2--->t1) l -> Expr Γ Δ ξ t2 l -> Expr Γ Δ ξ (t1) l
+ | ELam : ∀ Γ Δ ξ t1 t2 l ev, Expr Γ Δ (update_xi ξ l ((ev,t1)::nil)) t2 l -> Expr Γ Δ ξ (t1--->t2) l
+ | ELet : ∀ Γ Δ ξ tv t l ev,Expr Γ Δ ξ tv l ->Expr Γ Δ (update_xi ξ l ((ev,tv)::nil)) t l -> Expr Γ Δ ξ t l
+ | EEsc : ∀ Γ Δ ξ ec t l, Expr Γ Δ ξ (<[ ec |- t ]>) l -> Expr Γ Δ ξ t (ec::l)
+ | EBrak : ∀ Γ Δ ξ ec t l, Expr Γ Δ ξ t (ec::l) -> Expr Γ Δ ξ (<[ ec |- t ]>) l
+ | ECast : forall Γ Δ ξ t1 t2 (γ:HaskCoercion Γ Δ (t1 ∼∼∼ t2)) l, Expr Γ Δ ξ t1 l -> Expr Γ Δ ξ t2 l
+ | ENote : ∀ Γ Δ ξ t l, Note -> Expr Γ Δ ξ t l -> Expr Γ Δ ξ t l
+ | ETyApp : ∀ Γ Δ κ σ τ ξ l, Expr Γ Δ ξ (HaskTAll κ σ) l -> Expr Γ Δ ξ (substT σ τ) l
+ | ECoLam : forall Γ Δ κ σ (σ₁ σ₂:HaskType Γ κ) ξ l, Expr Γ (σ₁∼∼∼σ₂::Δ) ξ σ l -> Expr Γ Δ ξ (σ₁∼∼σ₂ ⇒ σ) l
+ | ECoApp : forall Γ Δ κ (σ₁ σ₂:HaskType Γ κ) (γ:HaskCoercion Γ Δ (σ₁∼∼∼σ₂)) σ ξ l, Expr Γ Δ ξ (σ₁ ∼∼ σ₂ ⇒ σ) l -> Expr Γ Δ ξ σ l
+ | ETyLam : ∀ Γ Δ ξ κ σ l n,
+ Expr (list_ins n κ Γ) (weakCE_ Δ) (weakLT_○ξ) (HaskTApp (weakF_ σ) (FreshHaskTyVar_ _)) (weakL_ l)-> Expr Γ Δ ξ (HaskTAll κ σ) l
+ | ECase : forall Γ Δ ξ l tc tbranches atypes,
+ Expr Γ Δ ξ (caseType tc atypes) l ->
+ Tree ??{ sac : _
+ & { scb : StrongCaseBranchWithVVs tc atypes sac
+ & Expr (sac_gamma sac Γ)
+ (sac_delta sac Γ atypes (weakCK'' Δ))
+ (scbwv_xi scb ξ l)
+ (weakT' tbranches)
+ (weakL' l) } } ->
+ Expr Γ Δ ξ tbranches l
+
+ | ELetRec : ∀ Γ Δ ξ l τ vars,
+ distinct (leaves (mapOptionTree (@fst _ _) vars)) ->
+ let ξ' := update_xi ξ l (leaves vars) in
+ ELetRecBindings Γ Δ ξ' l vars ->
+ Expr Γ Δ ξ' τ l ->
+ Expr Γ Δ ξ τ l