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).