Ltac Forall_pTree_from_elements :=
 cbv beta;
 unfold PTree.elements; simpl PTree.xelements;
 go_lower;
 repeat (( simple apply derives_extract_prop
                || simple apply derives_extract_prop');
                fancy_intros true);
 autorewrite with gather_prop;
 repeat (( simple apply derives_extract_prop
                || simple apply derives_extract_prop');
                fancy_intros true);
   repeat erewrite unfold_reptype_elim in * by reflexivity;
   try autorewrite with entailer_rewrite in *;
   repeat first
   [ apply prop_Forall_cons1;
     [unfold check_one_temp_spec, check_gvars_spec;
     simpl; auto;
     solve [normalize]
     | ]
   | apply prop_Forall_cons'
   | apply prop_Forall_cons
   | apply prop_Forall_nil'
   | apply prop_Forall_nil
   ];
 unfold check_one_temp_spec; simpl PTree.get.

(* Specifications: *)
Lemma exp_uncurry2: forall {T} {ND: NatDed T} A B C F, @exp T ND A (fun a => @exp T ND B (fun b => @exp T ND C (fun c => F a b c))) = @exp T ND (A*B*C) (fun x => F (fst (fst x)) (snd (fst x)) (snd x)).
Lemma exp_uncurry3: forall {T} {ND: NatDed T} A B C D F, @exp T ND A (fun a => @exp T ND B (fun b => @exp T ND C (fun c => @exp T ND D (fun d => F a b c d)))) = @exp T ND (A*B*C*D) (fun x => F (fst (fst (fst x))) (snd (fst (fst x))) (snd (fst x)) (snd x)).