diff options
Diffstat (limited to 'theories/Numbers/Natural/SpecViaZ')
| -rw-r--r-- | theories/Numbers/Natural/SpecViaZ/NSig.v | 2 | ||||
| -rw-r--r-- | theories/Numbers/Natural/SpecViaZ/NSigNAxioms.v | 11 |
2 files changed, 10 insertions, 3 deletions
diff --git a/theories/Numbers/Natural/SpecViaZ/NSig.v b/theories/Numbers/Natural/SpecViaZ/NSig.v index cfe842b9d..aaf44ca64 100644 --- a/theories/Numbers/Natural/SpecViaZ/NSig.v +++ b/theories/Numbers/Natural/SpecViaZ/NSig.v @@ -83,7 +83,7 @@ Module Type NType. Parameter spec_pred: forall x, [pred x] = Z.max 0 ([x] - 1). Parameter spec_sub: forall x y, [sub x y] = Z.max 0 ([x] - [y]). Parameter spec_mul: forall x y, [mul x y] = [x] * [y]. - Parameter spec_square: forall x, [square x] = [x] * [x]. + Parameter spec_square: forall x, [square x] = [x] * [x]. Parameter spec_pow_pos: forall x n, [pow_pos x n] = [x] ^ Zpos n. Parameter spec_pow_N: forall x n, [pow_N x n] = [x] ^ Z.of_N n. Parameter spec_pow: forall x n, [pow x n] = [x] ^ [n]. diff --git a/theories/Numbers/Natural/SpecViaZ/NSigNAxioms.v b/theories/Numbers/Natural/SpecViaZ/NSigNAxioms.v index adbd8223a..a0ad7643d 100644 --- a/theories/Numbers/Natural/SpecViaZ/NSigNAxioms.v +++ b/theories/Numbers/Natural/SpecViaZ/NSigNAxioms.v @@ -15,8 +15,8 @@ Module NTypeIsNAxioms (Import NN : NType'). Hint Rewrite spec_0 spec_1 spec_2 spec_succ spec_add spec_mul spec_pred spec_sub spec_div spec_modulo spec_gcd spec_compare spec_eqb spec_ltb spec_leb - spec_sqrt spec_log2 spec_max spec_min spec_pow_pos spec_pow_N spec_pow - spec_even spec_odd spec_testbit spec_shiftl spec_shiftr + spec_square spec_sqrt spec_log2 spec_max spec_min spec_pow_pos spec_pow_N + spec_pow spec_even spec_odd spec_testbit spec_shiftl spec_shiftr spec_land spec_lor spec_ldiff spec_lxor spec_div2 spec_of_N : nsimpl. Ltac nsimpl := autorewrite with nsimpl. @@ -256,6 +256,13 @@ Proof. intros. now zify. Qed. +(** Square *) + +Lemma square_spec n : square n == n * n. +Proof. + now zify. +Qed. + (** Sqrt *) Lemma sqrt_spec : forall n, 0<=n -> |