diff options
Diffstat (limited to 'lib')
-rw-r--r-- | lib/Coqlib.v | 7 | ||||
-rw-r--r-- | lib/Integers.v | 7 |
2 files changed, 14 insertions, 0 deletions
diff --git a/lib/Coqlib.v b/lib/Coqlib.v index 7bc4f8bf..02fa7bab 100644 --- a/lib/Coqlib.v +++ b/lib/Coqlib.v @@ -648,6 +648,13 @@ Proof. rewrite list_length_z_cons. omega. Qed. +Lemma list_length_z_map: + forall (A B: Type) (f: A -> B) (l: list A), + list_length_z (map f l) = list_length_z l. +Proof. + induction l. reflexivity. simpl. repeat rewrite list_length_z_cons. congruence. +Qed. + (** Extract the n-th element of a list, as [List.nth_error] does, but the index [n] is of type [Z]. *) diff --git a/lib/Integers.v b/lib/Integers.v index c54b6fe5..625973a0 100644 --- a/lib/Integers.v +++ b/lib/Integers.v @@ -871,6 +871,13 @@ Proof. apply neg_mul_distr_l. Qed. +Theorem mul_signed: + forall x y, mul x y = repr (signed x * signed y). +Proof. + intros; unfold mul. apply eqm_samerepr. + apply eqm_mult; apply eqm_sym; apply eqm_signed_unsigned. +Qed. + (** ** Properties of binary decompositions *) Lemma Z_shift_add_bin_decomp: |