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Integers.v: add unsigned_inj #289

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Integers.v: add unsigned_inj #289

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15 changes: 15 additions & 0 deletions lib/Integers.v
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Original file line number Diff line number Diff line change
Expand Up @@ -211,6 +211,21 @@ Definition one := repr 1.
Definition mone := repr (-1).
Definition iwordsize := repr zwordsize.

Lemma unsigned_inj : forall x y : int,
unsigned x = unsigned y -> x = y.
Proof.
intros [xval Hxrange] [yal Hyrange] E.
cbn in E. subst.
replace Hxrange with Hyrange; [subst; reflexivity|].
destruct Hxrange; destruct Hyrange.
f_equal; apply eq_proofs_unicity;
intros [] [];
match goal with
| |- ?x = ?x \/ ?x <> ?x => left; reflexivity
| |- ?x = ?y \/ ?x <> ?y => right; intro c; inversion c
end.
Qed.

Lemma mkint_eq:
forall x y Px Py, x = y -> mkint x Px = mkint y Py.
Proof.
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