diff options
| -rw-r--r-- | src/ModularArithmetic/ModularArithmeticTheorems.v | 6 | ||||
| -rw-r--r-- | src/ModularArithmetic/PrimeFieldTheorems.v | 9 |
2 files changed, 11 insertions, 4 deletions
diff --git a/src/ModularArithmetic/ModularArithmeticTheorems.v b/src/ModularArithmetic/ModularArithmeticTheorems.v index 4e0ba461e..5a84d80b7 100644 --- a/src/ModularArithmetic/ModularArithmeticTheorems.v +++ b/src/ModularArithmetic/ModularArithmeticTheorems.v @@ -150,14 +150,12 @@ Section FandZ. Qed. Require Crypto.Algebra. - Global Instance ring_modulo : @Algebra.ring (F m) Logic.eq (ZToField 0) (ZToField 1) opp add sub mul. + Global Instance commutative_ring_modulo : @Algebra.commutative_ring (F m) Logic.eq (ZToField 0) (ZToField 1) opp add sub mul. Proof. - repeat split; Fdefn. + repeat split; Fdefn; try apply F_eq_dec. { rewrite Z.add_0_r. auto. } - { apply F_eq_dec. } { rewrite <-Z.add_sub_swap, <-Z.add_sub_assoc, Z.sub_diag, Z.add_0_r. apply Z_mod_same_full. } { rewrite Z.mul_1_r. auto. } - { apply F_eq_dec. } Qed. Lemma ZToField_0 : @ZToField m 0 = 0. diff --git a/src/ModularArithmetic/PrimeFieldTheorems.v b/src/ModularArithmetic/PrimeFieldTheorems.v index 70a2c4a87..2021e8514 100644 --- a/src/ModularArithmetic/PrimeFieldTheorems.v +++ b/src/ModularArithmetic/PrimeFieldTheorems.v @@ -10,6 +10,7 @@ Require Import Coq.ZArith.BinInt Coq.NArith.BinNat Coq.ZArith.ZArith Coq.ZArith. Require Import Coq.Logic.Eqdep_dec. Require Import Crypto.Util.NumTheoryUtil Crypto.Util.ZUtil. Require Import Crypto.Util.Tactics. +Require Crypto.Algebra. Existing Class prime. @@ -51,6 +52,14 @@ Section FieldModuloPre. Proof. constructor; auto using Fring_theory, Fq_1_neq_0, F_mul_inv_l. Qed. + + Global Instance field_modulo : @Algebra.field (F q) Logic.eq (ZToField 0) (ZToField 1) opp add sub mul inv div. + Proof. + constructor; try solve_proper. + - apply commutative_ring_modulo. + - split. auto using F_mul_inv_l. + - split. auto using Fq_1_neq_0. + Qed. End FieldModuloPre. Module Type PrimeModulus. |