diff options
Diffstat (limited to 'src')
| -rw-r--r-- | src/Util/ZRange/BasicLemmas.v | 12 |
1 files changed, 12 insertions, 0 deletions
diff --git a/src/Util/ZRange/BasicLemmas.v b/src/Util/ZRange/BasicLemmas.v index d48c89011..6cfdaaff8 100644 --- a/src/Util/ZRange/BasicLemmas.v +++ b/src/Util/ZRange/BasicLemmas.v @@ -108,6 +108,18 @@ Module ZRange. -> is_bounded_by_bool (if b then x else y) (Operations.ZRange.union rx ry) = true. Proof. intros; apply is_bounded_by_bool_Proper_if_sumbool_union_dep; auto. Qed. + Lemma is_bounded_by_bool_Proper_if_bool_union_dep (b : bool) x y rx ry + : (b = true -> is_bounded_by_bool x rx = true) + -> (b = false -> is_bounded_by_bool y ry = true) + -> is_bounded_by_bool (if b then x else y) (Operations.ZRange.union rx ry) = true. + Proof. pose proof (is_bounded_by_bool_Proper_if_sumbool_union_dep (Sumbool.sumbool_of_bool b) x y rx ry); destruct b; assumption. Qed. + + Lemma is_bounded_by_bool_Proper_if_bool_union (b : bool) x y rx ry + : is_bounded_by_bool x rx = true + -> is_bounded_by_bool y ry = true + -> is_bounded_by_bool (if b then x else y) (Operations.ZRange.union rx ry) = true. + Proof. intros; apply is_bounded_by_bool_Proper_if_bool_union_dep; auto. Qed. + Lemma is_bounded_by_bool_opp x r : is_bounded_by_bool (Z.opp x) (ZRange.opp r) = is_bounded_by_bool x r. Proof. cbv [is_bounded_by_bool andb opp]; cbn [lower upper]; break_match; Z.ltb_to_lt; break_match; Z.ltb_to_lt; |