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-
-Require Import Zpower ZArith Znumtheory.
-Require Import Crypto.Galois.Galois Crypto.Galois.GaloisTheory.
-Require Import Crypto.Galois.ZGaloisField.
-
-Definition two_5_1 := (two_p 5) - 1.
-Lemma two_5_1_prime : prime two_5_1.
-Admitted.
-
-Definition two_127_1 := (two_p 127) - 1.
-Lemma two_127_1_prime : prime two_127_1.
-Admitted.
-
-Module Modulus31 <: Modulus.
- Definition modulus := exist _ two_5_1 two_5_1_prime.
-End Modulus31.
-
-Module Modulus127_1 <: Modulus.
- Definition modulus := exist _ two_127_1 two_127_1_prime.
-End Modulus127_1.
-
-Module Example31.
- Module Theory := ZGaloisField Modulus31.
- Import Theory.
- Local Open Scope GF_scope.
-
- Lemma example1: forall x y z: GF, z <> 0 -> x * (y / z) / z = x * y / (z ^ 2).
- Proof.
- intros; simpl.
- field; trivial.
- Qed.
-
- Lemma example2: forall x: GF, x * (inject 2) = x + x.
- Proof.
- intros; simpl.
- field.
- Qed.
-
- Lemma example3: forall x: GF, x ^ 2 + (inject 2) * x + (inject 1) = (x + (inject 1)) ^ 2.
- Proof.
- intros; simpl.
- field; trivial.
- Qed.
-
- Lemma example4: forall x: GF, x/(inject 1) = x.
- Proof.
- intros; field.
- discriminate.
- Qed.
-
-End Example31.
-
-Module TimesZeroTransparentTestModule.
- Module Theory := ZGaloisField Modulus127_1.
- Import Theory.
- Local Open Scope GF_scope.
-
- Lemma timesZero : forall a, a*0 = 0.
- intros.
- field.
- Qed.
-End TimesZeroTransparentTestModule.
-
-Module TimesZeroParametricTestModule (M: Modulus).
- Module Theory := ZGaloisField M.
- Import Theory.
- Local Open Scope GF_scope.
-
- Lemma timesZero : forall a, a*0 = 0.
- intros.
- field.
- Qed.
-End TimesZeroParametricTestModule.