Ltac do_repr_inj H :=
   simpl typeof in H;
  try first [apply typed_true_of_bool in H
               |apply typed_false_of_bool in H
               | apply typed_true_ptr in H
               | apply typed_false_ptr_e in H
               | apply typed_true_negb_bool_val_p in H
               | apply typed_false_negb_bool_val_p in H; [| solve [auto]]
               | apply typed_false_negb_bool_val_p' in H
               | unfold nullval in H; (*simple*) apply typed_true_tint_Vint in H
               | unfold nullval in H; (*simple*) apply typed_false_tint_Vint in H
(*               | simple apply typed_true_tint in H *)
               ];
   rewrite ?ptrofs_to_int_repr in H;
   repeat (rewrite -> negb_true_iff in H || rewrite -> negb_false_iff in H);
   try apply int_eq_e in H;
   match type of H with
(*  don't do these, because they weaken the statement, unfortunately.
          | _ <> _ => apply repr_neq_e (*int_eq_false_e*) in H
          | _ <> _ => apply repr64_neq_e in H
*)
          | _ <> _ => let H' := fresh H "'" in assert (H' := repr_neq_e _ _ H)
          | _ <> _ => let H' := fresh H "'" in assert (H' := repr64_neq_e _ _ H)
          | Int.eq _ _ = false => apply int_eq_false_e in H
          | _ => idtac
  end;
  first [ simple apply repr_inj_signed in H; [ | rep_omega | rep_omega ]
         | simple apply repr_inj_unsigned in H; [ | rep_omega | rep_omega ]
         | simple apply repr_inj_signed' in H; [ | rep_omega | rep_omega ]
         | simple apply repr_inj_unsigned' in H; [ | rep_omega | rep_omega ]
         | match type of H with
            | typed_true _  (force_val (sem_cmp_pp Ceq _ _)) =>
                                    apply typed_true_nullptr3 in H
            | typed_true _  (force_val (sem_cmp_pp Cne _ _)) =>
                                    apply typed_true_nullptr4 in H
            | typed_false _  (force_val (sem_cmp_pp Ceq _ _)) =>
                                    apply typed_false_nullptr3 in H
            | typed_false _  (force_val (sem_cmp_pp Cne _ _)) =>
                                    apply typed_false_nullptr4 in H
          end
         | apply typed_false_nullptr4 in H
         | simple apply ltu_repr in H; [ | rep_omega | rep_omega]
         | simple apply ltu_repr_false in H; [ | rep_omega | rep_omega]
         | simple apply ltu_inv in H; cleanup_repr H
         | simple apply ltu_false_inv in H; cleanup_repr H
         | simple apply lt_repr in H; [ | rep_omega | rep_omega]
         | simple apply lt_repr_false in H; [ | rep_omega | rep_omega]
         | simple apply lt_inv in H; cleanup_repr H
         | simple apply lt_false_inv in H; cleanup_repr H
         | idtac
         ];
    rewrite ?Byte_signed_lem, ?Byte_signed_lem',
                 ?int_repr_byte_signed_eq0, ?int_repr_byte_signed_eq0
      in H.Ltac simpl_fst_snd :=
repeat match goal with
| |- context [fst (?a,?b) ] => change (fst (a,b)) with a
| |- context [snd (?a,?b) ] => change (snd (a,b)) with b
end.Definition EXP_NAME := tt.Definition MARKED_ONE {A} (z: A) := z.Definition EXP_UNIT := tt.Ltac special_intros_EX :=
   match goal with
   | z := EXP_UNIT |- _ => clear z; cbv beta; intros _
   | z := EXP_NAME |- _ =>
         intro;
         match goal with a : ?x |- _ =>
             change x with (MARKED_ONE x) in a
         end;
         repeat match goal with
         | w := EXP_NAME, v := EXP_NAME, a: MARKED_ONE _ |- _ =>
           clear v; unfold MARKED_ONE in a;
           destruct a as [a v];
           match type of a with ?x =>
             change x with (MARKED_ONE x) in a
           end
         | v := EXP_NAME, a: MARKED_ONE _ |- _ =>
           clear v; unfold MARKED_ONE in a; rename a into v
         end;
         simpl_fst_snd
   end.

Lemma trivial_exp: forall P: environ -> mpred, P = exp (fun x: unit => P).