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Coq-Prime

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Ring RFth : (F_R pKfth).
Add
src
[ "From Coq Require Import Ring.", "From Coq Require Import Field_tac.", "From Coq Require Import Ring_tac.", "From Coq Require Import Eqdep_dec.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Ppow.", "From Coqprime Require Import GZnZ.", "Fro...
src/Coqprime/elliptic/ZEll.v
Ring
Field KFth : pKfth.
Add
src
[ "From Coq Require Import Ring.", "From Coq Require Import Field_tac.", "From Coq Require Import Ring_tac.", "From Coq Require Import Eqdep_dec.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Ppow.", "From Coqprime Require Import GZnZ.", "Fro...
src/Coqprime/elliptic/ZEll.v
Field
pNonSingular : 4 * pA * pA * pA + 27 * pB * pB <> 0. Proof. assert (F1 := p_pos). intros H; generalize (znz_inj _ _ _ H). unfold pkO,pkI,pA, pB, to_p, zero, one, pkplus, GZnZ.add, pkmul, mul, val. repeat match goal with |- ?t = 0 mod p -> _ => rmod t; auto end. rewrite (Zmod_small 0); auto with zarith. intros H1. apply...
Lemma
src
[ "From Coq Require Import Ring.", "From Coq Require Import Field_tac.", "From Coq Require Import Ring_tac.", "From Coq Require Import Eqdep_dec.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Ppow.", "From Coqprime Require Import GZnZ.", "Fro...
src/Coqprime/elliptic/ZEll.v
pNonSingular
pone_not_zero : 1 <> 0. Proof. intros H; generalize (znz_inj _ _ _ H); simpl val. repeat (rewrite Zmod_small); generalize (prime_ge_2 _ p_prime); auto with zarith. Qed.
Lemma
src
[ "From Coq Require Import Ring.", "From Coq Require Import Field_tac.", "From Coq Require Import Ring_tac.", "From Coq Require Import Eqdep_dec.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Ppow.", "From Coqprime Require Import GZnZ.", "Fro...
src/Coqprime/elliptic/ZEll.v
pone_not_zero
ptwo_not_zero : 2 <> 0. Proof. intros H; generalize (znz_inj _ _ _ H); simpl val. repeat (rewrite Zmod_small); generalize (prime_ge_2 _ p_prime); auto with zarith. intros H1; case (Zle_lt_or_eq _ _ H1); intros H2; auto with zarith. case N_not_div_2; rewrite H2; auto. Qed.
Lemma
src
[ "From Coq Require Import Ring.", "From Coq Require Import Field_tac.", "From Coq Require Import Ring_tac.", "From Coq Require Import Eqdep_dec.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Ppow.", "From Coqprime Require Import GZnZ.", "Fro...
src/Coqprime/elliptic/ZEll.v
ptwo_not_zero
pis_zero : pK -> bool. intros (k, Hk); case k; [exact true | idtac | idtac]; intros; exact false. Defined.
Definition
src
[ "From Coq Require Import Ring.", "From Coq Require Import Field_tac.", "From Coq Require Import Ring_tac.", "From Coq Require Import Eqdep_dec.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Ppow.", "From Coqprime Require Import GZnZ.", "Fro...
src/Coqprime/elliptic/ZEll.v
pis_zero
pis_zero_correct : forall k: pK, pis_zero k = true <-> k = 0. Proof. assert (F0 := p_pos). intros (k, Hk); generalize Hk; case k; simpl. intros Hk1; split; auto; intros H; unfold pkO, zero. apply (zirr p); rewrite Zmod_small; auto with zarith. intros Hk1; split; auto; intros H; try discriminate. intros Hk1; split; auto...
Lemma
src
[ "From Coq Require Import Ring.", "From Coq Require Import Field_tac.", "From Coq Require Import Ring_tac.", "From Coq Require Import Eqdep_dec.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Ppow.", "From Coqprime Require Import GZnZ.", "Fro...
src/Coqprime/elliptic/ZEll.v
pis_zero_correct
pell_theory : ell_theory pkO pkI pkplus pkmul pksub pkopp pkinv pkdiv pA pB pis_zero. Proof. constructor. apply pKfth. apply pNonSingular. exact pone_not_zero. exact ptwo_not_zero. exact pis_zero_correct. Qed.
Lemma
src
[ "From Coq Require Import Ring.", "From Coq Require Import Field_tac.", "From Coq Require Import Ring_tac.", "From Coq Require Import Eqdep_dec.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Ppow.", "From Coqprime Require Import GZnZ.", "Fro...
src/Coqprime/elliptic/ZEll.v
pell_theory
pG := (EFGroup pell_theory (uniq_all_znz _ p_pos) (in_all_znz _ p_pos)).
Definition
src
[ "From Coq Require Import Ring.", "From Coq Require Import Field_tac.", "From Coq Require Import Ring_tac.", "From Coq Require Import Eqdep_dec.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Ppow.", "From Coqprime Require Import GZnZ.", "Fro...
src/Coqprime/elliptic/ZEll.v
pG
gorder_pG : FGroup.g_order pG <= 2 * p + 1. Proof. replace p with (Z_of_nat (List.length (all_znz _ p_pos))). unfold pG; apply EFGroup_order. rewrite all_znz_length. generalize (prime_ge_2 _ p_prime). case p; simpl; auto. intros p1 Hp1; rewrite Zpos_eq_Z_of_nat_o_nat_of_P; auto. intros p1 HH; case HH; auto. Qed.
Lemma
src
[ "From Coq Require Import Ring.", "From Coq Require Import Field_tac.", "From Coq Require Import Ring_tac.", "From Coq Require Import Eqdep_dec.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Ppow.", "From Coqprime Require Import GZnZ.", "Fro...
src/Coqprime/elliptic/ZEll.v
gorder_pG
pelt := pelt pkI pkplus pkmul pA pB.
Let
src
[ "From Coq Require Import Ring.", "From Coq Require Import Field_tac.", "From Coq Require Import Ring_tac.", "From Coq Require Import Eqdep_dec.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Ppow.", "From Coqprime Require Import GZnZ.", "Fro...
src/Coqprime/elliptic/ZEll.v
pelt
mk_pelt := mk_pelt pkI pkplus pkmul pA pB.
Let
src
[ "From Coq Require Import Ring.", "From Coq Require Import Field_tac.", "From Coq Require Import Ring_tac.", "From Coq Require Import Eqdep_dec.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Ppow.", "From Coqprime Require Import GZnZ.", "Fro...
src/Coqprime/elliptic/ZEll.v
mk_pelt
is_zero_correct : forall x y, if (x ?= y) then x = y else x <> y. Proof. intros x y. apply Zeq_bool_if. Qed.
Lemma
src
[ "From Coq Require Import Ring.", "From Coq Require Import Field_tac.", "From Coq Require Import Ring_tac.", "From Coq Require Import Eqdep_dec.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Ppow.", "From Coqprime Require Import GZnZ.", "Fro...
src/Coqprime/elliptic/ZEll.v
is_zero_correct
inversible_is_not_k0 : forall x, [x] -> x :%p <> 0. Proof. intros x1 (k, Hk) H1. assert (F2: 2 < p). case (Zle_lt_or_eq _ _ (prime_ge_2 p p_prime)); auto. intros HH1; case N_not_div_2; rewrite HH1. apply p_div_N. assert (F3:= N_lt_2). injection H1; clear H1; rewrite (Zmod_small 0); auto with zarith; intros HH. absurd (...
Lemma
src
[ "From Coq Require Import Ring.", "From Coq Require Import Field_tac.", "From Coq Require Import Ring_tac.", "From Coq Require Import Eqdep_dec.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Ppow.", "From Coqprime Require Import GZnZ.", "Fro...
src/Coqprime/elliptic/ZEll.v
inversible_is_not_k0
inversible_is_zero : forall x, [x] -> pis_zero (x :%p) = false. Proof. intros x1 H1. case (pis_zero_correct (to_p x1)); case pis_zero; auto. intros HH _; generalize (HH (refl_equal true)); clear HH; intros HH. case (@inversible_is_not_k0 x1); auto. Qed.
Lemma
src
[ "From Coq Require Import Ring.", "From Coq Require Import Field_tac.", "From Coq Require Import Ring_tac.", "From Coq Require Import Eqdep_dec.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Ppow.", "From Coqprime Require Import GZnZ.", "Fro...
src/Coqprime/elliptic/ZEll.v
inversible_is_zero
to_p_nmul : forall x y, (x ** y):%p = x:%p * y:%p. Proof. intros x y. unfold nmul, to_p, pkmul, mul. unfold pK; apply zirr; simpl. assert (F1:= p_pos). rewrite <- Zmod_div_mod; auto. rewrite Zmult_mod; auto. generalize N_lt_2; auto with zarith. Qed.
Lemma
src
[ "From Coq Require Import Ring.", "From Coq Require Import Field_tac.", "From Coq Require Import Ring_tac.", "From Coq Require Import Eqdep_dec.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Ppow.", "From Coqprime Require Import GZnZ.", "Fro...
src/Coqprime/elliptic/ZEll.v
to_p_nmul
to_p_pow : forall x n, (x ^ (Z_of_nat n)):%p = pow pkI pkmul (x:%p) n. Proof. intros x n; elim n; clear n. simpl Z_of_nat; simpl pow; rewrite Zpower_0_r; auto. intros n Hrec; rewrite inj_S; unfold Z.succ; rewrite Zpower_exp; auto with zarith. assert (tmp: forall n x, pow 1 pkmul x (S n) = x * pow 1 pkmul x n). intros n...
Lemma
src
[ "From Coq Require Import Ring.", "From Coq Require Import Field_tac.", "From Coq Require Import Ring_tac.", "From Coq Require Import Eqdep_dec.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Ppow.", "From Coqprime Require Import GZnZ.", "Fro...
src/Coqprime/elliptic/ZEll.v
to_p_pow
to_p_nplus : forall x y, (x ++ y):%p = x:%p + y:%p. Proof. intros x y. unfold nplus, to_p, pkplus, GZnZ.add. unfold pK; apply zirr; simpl. assert (F1:= p_pos). rewrite <- Zmod_div_mod; auto. rewrite Zplus_mod; auto. generalize N_lt_2; auto with zarith. Qed.
Lemma
src
[ "From Coq Require Import Ring.", "From Coq Require Import Field_tac.", "From Coq Require Import Ring_tac.", "From Coq Require Import Eqdep_dec.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Ppow.", "From Coqprime Require Import GZnZ.", "Fro...
src/Coqprime/elliptic/ZEll.v
to_p_nplus
to_p_nsub : forall x y, (x -- y):%p = x:%p - y:%p. Proof. intros x y. unfold nsub, to_p, pksub, GZnZ.sub. unfold pK; apply zirr; simpl. assert (F1:= p_pos). rewrite <- Zmod_div_mod; auto. rewrite Zminus_mod; auto. generalize N_lt_2; auto with zarith. Qed.
Lemma
src
[ "From Coq Require Import Ring.", "From Coq Require Import Field_tac.", "From Coq Require Import Ring_tac.", "From Coq Require Import Eqdep_dec.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Ppow.", "From Coqprime Require Import GZnZ.", "Fro...
src/Coqprime/elliptic/ZEll.v
to_p_nsub
to_p_2 : 2:%p = 2. Proof. unfold to_p, pkplus, pkI, GZnZ.add, pK; apply zirr; simpl. assert (F1:= p_pos). rewrite <- Zplus_mod; auto. Qed.
Lemma
src
[ "From Coq Require Import Ring.", "From Coq Require Import Field_tac.", "From Coq Require Import Ring_tac.", "From Coq Require Import Eqdep_dec.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Ppow.", "From Coqprime Require Import GZnZ.", "Fro...
src/Coqprime/elliptic/ZEll.v
to_p_2
to_p_3 : 3:%p = 3. Proof. unfold to_p, pkplus, pkI, GZnZ.add, pK; apply zirr; simpl. assert (F1:= p_pos). repeat match goal with |- _ = ?t => rmod t; auto end. Qed.
Lemma
src
[ "From Coq Require Import Ring.", "From Coq Require Import Field_tac.", "From Coq Require Import Ring_tac.", "From Coq Require Import Eqdep_dec.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Ppow.", "From Coqprime Require Import GZnZ.", "Fro...
src/Coqprime/elliptic/ZEll.v
to_p_3
to_p_tac := repeat (rewrite to_p_nmul || rewrite to_p_nplus || rewrite to_p_nsub || rewrite to_p_2 || rewrite to_p_3); auto.
Ltac
src
[ "From Coq Require Import Ring.", "From Coq Require Import Field_tac.", "From Coq Require Import Ring_tac.", "From Coq Require Import Eqdep_dec.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Ppow.", "From Coqprime Require Import GZnZ.", "Fro...
src/Coqprime/elliptic/ZEll.v
to_p_tac
inversible_kO : forall z1 z2, z2 = 0 -> z1:%p = z2 -> [z1] -> False. Proof. intros z1 z2 H1 H2 H3. generalize (inversible_is_not_k0 H3). rewrite H2; rewrite H1. intros H; case H; auto. Qed.
Lemma
src
[ "From Coq Require Import Ring.", "From Coq Require Import Field_tac.", "From Coq Require Import Ring_tac.", "From Coq Require Import Eqdep_dec.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Ppow.", "From Coqprime Require Import GZnZ.", "Fro...
src/Coqprime/elliptic/ZEll.v
inversible_kO
pdouble : pelt -> pelt := pdouble (pell_theory).
Let
src
[ "From Coq Require Import Ring.", "From Coq Require Import Field_tac.", "From Coq Require Import Ring_tac.", "From Coq Require Import Eqdep_dec.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Ppow.", "From Coqprime Require Import GZnZ.", "Fro...
src/Coqprime/elliptic/ZEll.v
pdouble
padd : pelt -> pelt -> pelt := padd (pell_theory).
Let
src
[ "From Coq Require Import Ring.", "From Coq Require Import Field_tac.", "From Coq Require Import Ring_tac.", "From Coq Require Import Eqdep_dec.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Ppow.", "From Coqprime Require Import GZnZ.", "Fro...
src/Coqprime/elliptic/ZEll.v
padd
elt := (elt pkI pkplus pkmul pA pB).
Let
src
[ "From Coq Require Import Ring.", "From Coq Require Import Field_tac.", "From Coq Require Import Ring_tac.", "From Coq Require Import Eqdep_dec.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Ppow.", "From Coqprime Require Import GZnZ.", "Fro...
src/Coqprime/elliptic/ZEll.v
elt
inf_elt := (inf_elt pkI pkplus pkmul pA pB).
Let
src
[ "From Coq Require Import Ring.", "From Coq Require Import Field_tac.", "From Coq Require Import Ring_tac.", "From Coq Require Import Eqdep_dec.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Ppow.", "From Coqprime Require Import GZnZ.", "Fro...
src/Coqprime/elliptic/ZEll.v
inf_elt
curve_elt := (curve_elt pkI pkplus pkmul pA pB).
Let
src
[ "From Coq Require Import Ring.", "From Coq Require Import Field_tac.", "From Coq Require Import Ring_tac.", "From Coq Require Import Eqdep_dec.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Ppow.", "From Coqprime Require Import GZnZ.", "Fro...
src/Coqprime/elliptic/ZEll.v
curve_elt
equiv : nelt -> elt -> Prop := z_equiv:equiv nzero inf_elt | n_equiv: forall x y z x1 y1 H, x:%p / z:%p = x1 -> y:%p / z:%p = y1 -> equiv (ntriple x y z) (@curve_elt x1 y1 H). Infix "=~~=" := equiv (at level 40, no associativity).
Inductive
src
[ "From Coq Require Import Ring.", "From Coq Require Import Field_tac.", "From Coq Require Import Ring_tac.", "From Coq Require Import Eqdep_dec.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Ppow.", "From Coqprime Require Import GZnZ.", "Fro...
src/Coqprime/elliptic/ZEll.v
equiv
pe2e := pe2e pell_theory.
Let
src
[ "From Coq Require Import Ring.", "From Coq Require Import Field_tac.", "From Coq Require Import Ring_tac.", "From Coq Require Import Eqdep_dec.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Ppow.", "From Coqprime Require Import GZnZ.", "Fro...
src/Coqprime/elliptic/ZEll.v
pe2e
add := add pell_theory.
Let
src
[ "From Coq Require Import Ring.", "From Coq Require Import Field_tac.", "From Coq Require Import Ring_tac.", "From Coq Require Import Eqdep_dec.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Ppow.", "From Coqprime Require Import GZnZ.", "Fro...
src/Coqprime/elliptic/ZEll.v
add
opp := opp pell_theory.
Let
src
[ "From Coq Require Import Ring.", "From Coq Require Import Field_tac.", "From Coq Require Import Ring_tac.", "From Coq Require Import Eqdep_dec.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Ppow.", "From Coqprime Require Import GZnZ.", "Fro...
src/Coqprime/elliptic/ZEll.v
opp
pow := pow pkI pkmul.
Let
src
[ "From Coq Require Import Ring.", "From Coq Require Import Field_tac.", "From Coq Require Import Ring_tac.", "From Coq Require Import Eqdep_dec.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Ppow.", "From Coqprime Require Import GZnZ.", "Fro...
src/Coqprime/elliptic/ZEll.v
pow
nedouble_correct : forall sc n1 p1, n1 =~~= p1 -> [[ndouble sc n1]] -> fst (ndouble sc n1) =~~= add p1 p1. Proof. intros sc n1 p1 H; inversion_clear H. simpl; intros; constructor. intros V1. case (nInversible_double _ _ V1); intros V2 _. inversion_clear V2. simpl. case Kdec; [idtac | intros HH; case HH]; auto. intros e...
Lemma
src
[ "From Coq Require Import Ring.", "From Coq Require Import Field_tac.", "From Coq Require Import Ring_tac.", "From Coq Require Import Eqdep_dec.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Ppow.", "From Coqprime Require Import GZnZ.", "Fro...
src/Coqprime/elliptic/ZEll.v
nedouble_correct
neadd_correct : forall sc n1 p1 n2 p2, n1 =~~= p1 -> n2 =~~= p2 -> [[nadd sc n1 n2]] -> fst (nadd sc n1 n2) =~~= add p1 p2. Proof. intros sc n1 p1 n2 p2 H; inversion_clear H. simpl; auto. intros H; inversion_clear H. simpl; intros; constructor; auto. intros V1. case (nInversible_add _ _ _ V1); intros V2 (V3, _). invers...
Lemma
src
[ "From Coq Require Import Ring.", "From Coq Require Import Field_tac.", "From Coq Require Import Ring_tac.", "From Coq Require Import Eqdep_dec.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Ppow.", "From Coqprime Require Import GZnZ.", "Fro...
src/Coqprime/elliptic/ZEll.v
neadd_correct
nopp_correct : forall a1 p1, a1 =~~= p1 -> [[(a1,1%Z)]] -> nopp a1 =~~= opp p1. Proof. assert (F0: 0 < p); auto with zarith. intros a1 p1 H; inversion_clear H; simpl; constructor; auto. rewrite <- H2. field_simplify_eq; auto. unfold ninv, pkopp, GZnZ.opp, to_p, pK; apply zirr. simpl; rewrite <- Zmod_div_mod; auto with ...
Lemma
src
[ "From Coq Require Import Ring.", "From Coq Require Import Field_tac.", "From Coq Require Import Ring_tac.", "From Coq Require Import Eqdep_dec.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Ppow.", "From Coqprime Require Import GZnZ.", "Fro...
src/Coqprime/elliptic/ZEll.v
nopp_correct
scalb_correct : forall p sc b a1 p1, a1 =~~= p1 -> [[scalb sc b a1 p]] -> fst (scalb sc b a1 p) =~~= EGroup.gpow p1 pG (if b then (Pos.succ p) else p). Proof. assert (F0: forall p1, List.In p1 (FGroup.s pG)). intros p1. apply (FELLK_in pell_theory _ (in_all_znz _ p_pos)). intros p0; unfold scalb; elim p0; clear p0; fol...
Lemma
src
[ "From Coq Require Import Ring.", "From Coq Require Import Field_tac.", "From Coq Require Import Ring_tac.", "From Coq Require Import Eqdep_dec.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Ppow.", "From Coqprime Require Import GZnZ.", "Fro...
src/Coqprime/elliptic/ZEll.v
scalb_correct
scal_correct : forall p sc a1 p1, a1 =~~= p1 -> [[scal sc a1 p]] -> fst (scal sc a1 p) =~~= EGroup.gpow p1 pG p. Proof. intros p1 sc; exact (scalb_correct p1 sc false). Qed.
Lemma
src
[ "From Coq Require Import Ring.", "From Coq Require Import Field_tac.", "From Coq Require Import Ring_tac.", "From Coq Require Import Eqdep_dec.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Ppow.", "From Coqprime Require Import GZnZ.", "Fro...
src/Coqprime/elliptic/ZEll.v
scal_correct
scal_list_correct : forall l sc a1 p1, a1 =~~= p1 -> [[scal_list sc a1 l]] -> fst (scal_list sc a1 l) =~~= EGroup.gpow p1 pG (Zmull l). Proof. assert (F0: forall p1, List.In p1 (FGroup.s pG)). intros p1. apply (FELLK_in pell_theory _ (in_all_znz _ p_pos)). intros l; elim l; auto; clear l. intros sc a1 p1 H H1. change (...
Lemma
src
[ "From Coq Require Import Ring.", "From Coq Require Import Field_tac.", "From Coq Require Import Ring_tac.", "From Coq Require Import Eqdep_dec.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Ppow.", "From Coqprime Require Import GZnZ.", "Fro...
src/Coqprime/elliptic/ZEll.v
scal_list_correct
scalL_not_1 : forall l sc a p1 n, a =~~= p1 -> [[scalL sc a l]] -> List.In n l -> gpow p1 pG (Zmull l / n) <> pG.(FGroup.e). Proof. assert (F0: forall p1, List.In p1 (FGroup.s pG)). intros p1. apply (FELLK_in pell_theory _ (in_all_znz _ p_pos)). intros l; elim l; auto; clear l. simpl (List.In). intros a l Hrec sc a1 p1...
Lemma
src
[ "From Coq Require Import Ring.", "From Coq Require Import Field_tac.", "From Coq Require Import Ring_tac.", "From Coq Require Import Eqdep_dec.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Ppow.", "From Coqprime Require Import GZnZ.", "Fro...
src/Coqprime/elliptic/ZEll.v
scalL_not_1
scalL_1 : forall l sc a p1, a =~~= p1 -> [[scalL sc a l]] -> fst (scalL sc a l) =~~= gpow p1 pG (Zmull l). Proof. assert (F0: forall p1, List.In p1 (FGroup.s pG)). intros p1. apply (FELLK_in pell_theory _ (in_all_znz _ p_pos)). intros l; elim l; auto; clear l. simpl scalL; simpl fst; simpl Zmull. unfold Zmull; simpl Li...
Lemma
src
[ "From Coq Require Import Ring.", "From Coq Require Import Field_tac.", "From Coq Require Import Ring_tac.", "From Coq Require Import Eqdep_dec.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Ppow.", "From Coqprime Require Import GZnZ.", "Fro...
src/Coqprime/elliptic/ZEll.v
scalL_1
itac := match goal with H: inversible _ (_ ** _) |- _ => case (inversible_mult_inv N_lt_2 _ _ H); clear H; let H1 := fresh "NI" in let H2 := fresh "NI" in intros H1 H2 | |- inversible _ (_ ** _) => apply inversible_mult end; auto.
Ltac
src
[ "From Coq Require Import Ring.", "From Coq Require Import Field_tac.", "From Coq Require Import Ring_tac.", "From Coq Require Import Eqdep_dec.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Ppow.", "From Coqprime Require Import GZnZ.", "Fro...
src/Coqprime/elliptic/ZEll.v
itac
z2p x := match x with Zpos p => p | Zneg p => p | Z0 => xH end.
Let
src
[ "From Coq Require Import Ring.", "From Coq Require Import Field_tac.", "From Coq Require Import Ring_tac.", "From Coq Require Import Eqdep_dec.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Ppow.", "From Coqprime Require Import GZnZ.", "Fro...
src/Coqprime/elliptic/ZEll.v
z2p
scalL_prime : let a := ntriple x y 1 in let isc := 4 ** A ** A ** A ++ 27 ** B ** B in let (a1, sc1) := scal N A isc a F in let (S1,R1) := psplit lR in let (a2, sc2) := scal N A sc1 a1 S1 in let (a3, sc3) := scalL N A sc2 a2 R1 in match a3 with nzero => if (Zeq_bool (Z.gcd sc3 N) 1) then prime N else True | _ => True e...
Lemma
src
[ "From Coq Require Import Ring.", "From Coq Require Import Field_tac.", "From Coq Require Import Ring_tac.", "From Coq Require Import Eqdep_dec.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Ppow.", "From Coqprime Require Import GZnZ.", "Fro...
src/Coqprime/elliptic/ZEll.v
scalL_prime
enc t := vm_cast_no_check t.
Ltac
src
[ "From Coq Require Import List.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Pock." ]
src/Coqprime/examples/BasePrimes.v
enc
prime2 : prime 2. exact prime_2. Qed.
Lemma
src
[ "From Coq Require Import List.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Pock." ]
src/Coqprime/examples/BasePrimes.v
prime2
prime3 : prime 3. Proof. apply (Pocklington_refl (Pock_certif 3 2 ((2,1)::nil) 1) ((Proof_certif 2 prime2) :: nil)). enc (refl_equal true). Qed.
Lemma
src
[ "From Coq Require Import List.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Pock." ]
src/Coqprime/examples/BasePrimes.v
prime3
prime5 : prime 5. Proof. apply (Pocklington_refl (Pock_certif 5 2 ((2,2)::nil) 1) ((Proof_certif 2 prime2) :: nil)). enc (refl_equal true). Qed.
Lemma
src
[ "From Coq Require Import List.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Pock." ]
src/Coqprime/examples/BasePrimes.v
prime5
prime7 : prime 7. Proof. apply (Pocklington_refl (Pock_certif 7 3 ((2,1)::nil) 1) ((Proof_certif 2 prime2) :: nil)). enc (refl_equal true). Qed.
Lemma
src
[ "From Coq Require Import List.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Pock." ]
src/Coqprime/examples/BasePrimes.v
prime7
prime11 : prime 11. Proof. apply (Pocklington_refl (Pock_certif 11 2 ((2,1)::nil) 1) ((Proof_certif 2 prime2) :: nil)). enc (refl_equal true). Qed.
Lemma
src
[ "From Coq Require Import List.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Pock." ]
src/Coqprime/examples/BasePrimes.v
prime11
prime13 : prime 13. Proof. apply (Pocklington_refl (Pock_certif 13 2 ((2,2)::nil) 1) ((Proof_certif 2 prime2) :: nil)). enc (refl_equal true). Qed.
Lemma
src
[ "From Coq Require Import List.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Pock." ]
src/Coqprime/examples/BasePrimes.v
prime13
prime17 : prime 17. Proof. apply (Pocklington_refl (Pock_certif 17 3 ((2,4)::nil) 1) ((Proof_certif 2 prime2) :: nil)). enc (refl_equal true). Qed.
Lemma
src
[ "From Coq Require Import List.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Pock." ]
src/Coqprime/examples/BasePrimes.v
prime17
prime19 : prime 19. Proof. apply (Pocklington_refl (Pock_certif 19 2 ((2,1)::nil) 1) ((Proof_certif 2 prime2) :: nil)). enc (refl_equal true). Qed.
Lemma
src
[ "From Coq Require Import List.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Pock." ]
src/Coqprime/examples/BasePrimes.v
prime19
prime23 : prime 23. Proof. apply (Pocklington_refl (Pock_certif 23 5 ((2,1)::nil) 1) ((Proof_certif 2 prime2) :: nil)). enc (refl_equal true). Qed.
Lemma
src
[ "From Coq Require Import List.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Pock." ]
src/Coqprime/examples/BasePrimes.v
prime23
prime29 : prime 29. Proof. apply (Pocklington_refl (Pock_certif 29 2 ((2,2)::nil) 1) ((Proof_certif 2 prime2) :: nil)). enc (refl_equal true). Qed.
Lemma
src
[ "From Coq Require Import List.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Pock." ]
src/Coqprime/examples/BasePrimes.v
prime29
prime31 : prime 31. Proof. apply (Pocklington_refl (Pock_certif 31 3 ((2,1)::nil) 1) ((Proof_certif 2 prime2) :: nil)). enc (refl_equal true). Qed.
Lemma
src
[ "From Coq Require Import List.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Pock." ]
src/Coqprime/examples/BasePrimes.v
prime31
prime37 : prime 37. Proof. apply (Pocklington_refl (Pock_certif 37 2 ((2,2)::nil) 1) ((Proof_certif 2 prime2) :: nil)). enc (refl_equal true). Qed.
Lemma
src
[ "From Coq Require Import List.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Pock." ]
src/Coqprime/examples/BasePrimes.v
prime37
prime41 : prime 41. Proof. apply (Pocklington_refl (Pock_certif 41 3 ((2,3)::nil) 1) ((Proof_certif 2 prime2) :: nil)). enc (refl_equal true). Qed.
Lemma
src
[ "From Coq Require Import List.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Pock." ]
src/Coqprime/examples/BasePrimes.v
prime41
prime43 : prime 43. Proof. apply (Pocklington_refl (Pock_certif 43 3 ((3, 1)::(2,1)::nil) 1) ((Proof_certif 3 prime3) :: (Proof_certif 2 prime2) :: nil)). enc (refl_equal true). Qed.
Lemma
src
[ "From Coq Require Import List.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Pock." ]
src/Coqprime/examples/BasePrimes.v
prime43
prime47 : prime 47. Proof. apply (Pocklington_refl (Pock_certif 47 5 ((23, 1)::(2,1)::nil) 1) ((Proof_certif 23 prime23) :: (Proof_certif 2 prime2) :: nil)). enc (refl_equal true). Qed.
Lemma
src
[ "From Coq Require Import List.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Pock." ]
src/Coqprime/examples/BasePrimes.v
prime47
prime53 : prime 53. Proof. apply (Pocklington_refl (Pock_certif 53 2 ((2,2)::nil) 4) ((Proof_certif 2 prime2) :: nil)). enc (refl_equal true). Qed.
Lemma
src
[ "From Coq Require Import List.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Pock." ]
src/Coqprime/examples/BasePrimes.v
prime53
prime59 : prime 59. Proof. apply (Pocklington_refl (Pock_certif 59 2 ((29, 1)::(2,1)::nil) 1) ((Proof_certif 29 prime29) :: (Proof_certif 2 prime2) :: nil)). enc (refl_equal true). Qed.
Lemma
src
[ "From Coq Require Import List.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Pock." ]
src/Coqprime/examples/BasePrimes.v
prime59
prime61 : prime 61. Proof. apply (Pocklington_refl (Pock_certif 61 2 ((2,2)::nil) 6) ((Proof_certif 2 prime2) :: nil)). enc (refl_equal true). Qed.
Lemma
src
[ "From Coq Require Import List.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Pock." ]
src/Coqprime/examples/BasePrimes.v
prime61
prime67 : prime 67. Proof. apply (Pocklington_refl (Pock_certif 67 2 ((3, 1)::(2,1)::nil) 1) ((Proof_certif 3 prime3) :: (Proof_certif 2 prime2) :: nil)). enc (refl_equal true). Qed.
Lemma
src
[ "From Coq Require Import List.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Pock." ]
src/Coqprime/examples/BasePrimes.v
prime67
prime71 : prime 71. Proof. apply (Pocklington_refl (Pock_certif 71 7 ((5, 1)::(2,1)::nil) 1) ((Proof_certif 5 prime5) :: (Proof_certif 2 prime2) :: nil)). enc (refl_equal true). Qed.
Lemma
src
[ "From Coq Require Import List.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Pock." ]
src/Coqprime/examples/BasePrimes.v
prime71
prime73 : prime 73. Proof. apply (Pocklington_refl (Pock_certif 73 5 ((2,3)::nil) 1) ((Proof_certif 2 prime2) :: nil)). enc (refl_equal true). Qed.
Lemma
src
[ "From Coq Require Import List.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Pock." ]
src/Coqprime/examples/BasePrimes.v
prime73
prime79 : prime 79. Proof. apply (Pocklington_refl (Pock_certif 79 3 ((3, 1)::(2,1)::nil) 1) ((Proof_certif 3 prime3) :: (Proof_certif 2 prime2) :: nil)). enc (refl_equal true). Qed.
Lemma
src
[ "From Coq Require Import List.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Pock." ]
src/Coqprime/examples/BasePrimes.v
prime79
prime83 : prime 83. Proof. apply (Pocklington_refl (Pock_certif 83 2 ((41, 1)::(2,1)::nil) 1) ((Proof_certif 41 prime41) :: (Proof_certif 2 prime2) :: nil)). enc (refl_equal true). Qed.
Lemma
src
[ "From Coq Require Import List.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Pock." ]
src/Coqprime/examples/BasePrimes.v
prime83
prime89 : prime 89. Proof. apply (Pocklington_refl (Pock_certif 89 3 ((2,3)::nil) 1) ((Proof_certif 2 prime2) :: nil)). enc (refl_equal true). Qed.
Lemma
src
[ "From Coq Require Import List.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Pock." ]
src/Coqprime/examples/BasePrimes.v
prime89
prime97 : prime 97. Proof. apply (Pocklington_refl (Pock_certif 97 5 ((2,5)::nil) 1) ((Proof_certif 2 prime2) :: nil)). enc (refl_equal true). Qed.
Lemma
src
[ "From Coq Require Import List.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Pock." ]
src/Coqprime/examples/BasePrimes.v
prime97
prime101 : prime 101. Proof. apply (Pocklington_refl (Pock_certif 101 2 ((2,2)::nil) 1) ((Proof_certif 2 prime2) :: nil)). enc (refl_equal true). Qed.
Lemma
src
[ "From Coq Require Import List.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Pock." ]
src/Coqprime/examples/BasePrimes.v
prime101
prime103 : prime 103. Proof. apply (Pocklington_refl (Pock_certif 103 5 ((3, 1)::(2,1)::nil) 4) ((Proof_certif 3 prime3) :: (Proof_certif 2 prime2) :: nil)). enc (refl_equal true). Qed.
Lemma
src
[ "From Coq Require Import List.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Pock." ]
src/Coqprime/examples/BasePrimes.v
prime103
prime107 : prime 107. Proof. apply (Pocklington_refl (Pock_certif 107 2 ((53, 1)::(2,1)::nil) 1) ((Proof_certif 53 prime53) :: (Proof_certif 2 prime2) :: nil)). enc (refl_equal true). Qed.
Lemma
src
[ "From Coq Require Import List.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Pock." ]
src/Coqprime/examples/BasePrimes.v
prime107
prime109 : prime 109. Proof. apply (Pocklington_refl (Pock_certif 109 2 ((2,2)::nil) 1) ((Proof_certif 2 prime2) :: nil)). enc (refl_equal true). Qed.
Lemma
src
[ "From Coq Require Import List.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Pock." ]
src/Coqprime/examples/BasePrimes.v
prime109
prime113 : prime 113. Proof. apply (Pocklington_refl (Pock_certif 113 3 ((2,4)::nil) 1) ((Proof_certif 2 prime2) :: nil)). enc (refl_equal true). Qed.
Lemma
src
[ "From Coq Require Import List.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Pock." ]
src/Coqprime/examples/BasePrimes.v
prime113
prime127 : prime 127. Proof. apply (Pocklington_refl (Pock_certif 127 3 ((3, 1)::(2,1)::nil) 8) ((Proof_certif 3 prime3) :: (Proof_certif 2 prime2) :: nil)). enc (refl_equal true). Qed.
Lemma
src
[ "From Coq Require Import List.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Pock." ]
src/Coqprime/examples/BasePrimes.v
prime127
prime131 : prime 131. Proof. apply (Pocklington_refl (Pock_certif 131 2 ((5, 1)::(2,1)::nil) 1) ((Proof_certif 5 prime5) :: (Proof_certif 2 prime2) :: nil)). enc (refl_equal true). Qed.
Lemma
src
[ "From Coq Require Import List.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Pock." ]
src/Coqprime/examples/BasePrimes.v
prime131
prime137 : prime 137. Proof. apply (Pocklington_refl (Pock_certif 137 3 ((2,3)::nil) 1) ((Proof_certif 2 prime2) :: nil)). enc (refl_equal true). Qed.
Lemma
src
[ "From Coq Require Import List.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Pock." ]
src/Coqprime/examples/BasePrimes.v
prime137
prime139 : prime 139. Proof. apply (Pocklington_refl (Pock_certif 139 2 ((3, 1)::(2,1)::nil) 10) ((Proof_certif 3 prime3) :: (Proof_certif 2 prime2) :: nil)). enc (refl_equal true). Qed.
Lemma
src
[ "From Coq Require Import List.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Pock." ]
src/Coqprime/examples/BasePrimes.v
prime139
prime149 : prime 149. Proof. apply (Pocklington_refl (Pock_certif 149 2 ((2,2)::nil) 1) ((Proof_certif 2 prime2) :: nil)). enc (refl_equal true). Qed.
Lemma
src
[ "From Coq Require Import List.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Pock." ]
src/Coqprime/examples/BasePrimes.v
prime149
prime151 : prime 151. Proof. apply (Pocklington_refl (Pock_certif 151 6 ((3, 1)::(2,1)::nil) 1) ((Proof_certif 3 prime3) :: (Proof_certif 2 prime2) :: nil)). enc (refl_equal true). Qed.
Lemma
src
[ "From Coq Require Import List.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Pock." ]
src/Coqprime/examples/BasePrimes.v
prime151
prime157 : prime 157. Proof. apply (Pocklington_refl (Pock_certif 157 2 ((2,2)::nil) 4) ((Proof_certif 2 prime2) :: nil)). enc (refl_equal true). Qed.
Lemma
src
[ "From Coq Require Import List.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Pock." ]
src/Coqprime/examples/BasePrimes.v
prime157
prime163 : prime 163. Proof. apply (Pocklington_refl (Pock_certif 163 2 ((3, 1)::(2,1)::nil) 1) ((Proof_certif 3 prime3) :: (Proof_certif 2 prime2) :: nil)). enc (refl_equal true). Qed.
Lemma
src
[ "From Coq Require Import List.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Pock." ]
src/Coqprime/examples/BasePrimes.v
prime163
prime167 : prime 167. Proof. apply (Pocklington_refl (Pock_certif 167 5 ((83, 1)::(2,1)::nil) 1) ((Proof_certif 83 prime83) :: (Proof_certif 2 prime2) :: nil)). enc (refl_equal true). Qed.
Lemma
src
[ "From Coq Require Import List.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Pock." ]
src/Coqprime/examples/BasePrimes.v
prime167
prime173 : prime 173. Proof. apply (Pocklington_refl (Pock_certif 173 2 ((2,2)::nil) 1) ((Proof_certif 2 prime2) :: nil)). enc (refl_equal true). Qed.
Lemma
src
[ "From Coq Require Import List.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Pock." ]
src/Coqprime/examples/BasePrimes.v
prime173
prime179 : prime 179. Proof. apply (Pocklington_refl (Pock_certif 179 2 ((89, 1)::(2,1)::nil) 1) ((Proof_certif 89 prime89) :: (Proof_certif 2 prime2) :: nil)). enc (refl_equal true). Qed.
Lemma
src
[ "From Coq Require Import List.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Pock." ]
src/Coqprime/examples/BasePrimes.v
prime179
prime181 : prime 181. Proof. apply (Pocklington_refl (Pock_certif 181 2 ((2,2)::nil) 1) ((Proof_certif 2 prime2) :: nil)). enc (refl_equal true). Qed.
Lemma
src
[ "From Coq Require Import List.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Pock." ]
src/Coqprime/examples/BasePrimes.v
prime181
prime191 : prime 191. Proof. apply (Pocklington_refl (Pock_certif 191 7 ((5, 1)::(2,1)::nil) 1) ((Proof_certif 5 prime5) :: (Proof_certif 2 prime2) :: nil)). enc (refl_equal true). Qed.
Lemma
src
[ "From Coq Require Import List.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Pock." ]
src/Coqprime/examples/BasePrimes.v
prime191
prime193 : prime 193. Proof. apply (Pocklington_refl (Pock_certif 193 5 ((2,6)::nil) 1) ((Proof_certif 2 prime2) :: nil)). enc (refl_equal true). Qed.
Lemma
src
[ "From Coq Require Import List.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Pock." ]
src/Coqprime/examples/BasePrimes.v
prime193
prime197 : prime 197. Proof. apply (Pocklington_refl (Pock_certif 197 2 ((7, 1)::(2,2)::nil) 1) ((Proof_certif 7 prime7) :: (Proof_certif 2 prime2) :: nil)). enc (refl_equal true). Qed.
Lemma
src
[ "From Coq Require Import List.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Pock." ]
src/Coqprime/examples/BasePrimes.v
prime197
prime199 : prime 199. Proof. apply (Pocklington_refl (Pock_certif 199 3 ((3, 1)::(2,1)::nil) 8) ((Proof_certif 3 prime3) :: (Proof_certif 2 prime2) :: nil)). enc (refl_equal true). Qed.
Lemma
src
[ "From Coq Require Import List.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Pock." ]
src/Coqprime/examples/BasePrimes.v
prime199
prime211 : prime 211. Proof. apply (Pocklington_refl (Pock_certif 211 2 ((3, 1)::(2,1)::nil) 10) ((Proof_certif 3 prime3) :: (Proof_certif 2 prime2) :: nil)). enc (refl_equal true). Qed.
Lemma
src
[ "From Coq Require Import List.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Pock." ]
src/Coqprime/examples/BasePrimes.v
prime211
prime223 : prime 223. Proof. apply (Pocklington_refl (Pock_certif 223 3 ((3, 1)::(2,1)::nil) 1) ((Proof_certif 3 prime3) :: (Proof_certif 2 prime2) :: nil)). enc (refl_equal true). Qed.
Lemma
src
[ "From Coq Require Import List.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Pock." ]
src/Coqprime/examples/BasePrimes.v
prime223
prime227 : prime 227. Proof. apply (Pocklington_refl (Pock_certif 227 2 ((113, 1)::(2,1)::nil) 1) ((Proof_certif 113 prime113) :: (Proof_certif 2 prime2) :: nil)). enc (refl_equal true). Qed.
Lemma
src
[ "From Coq Require Import List.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Pock." ]
src/Coqprime/examples/BasePrimes.v
prime227
prime229 : prime 229. Proof. apply (Pocklington_refl (Pock_certif 229 6 ((3, 1)::(2,2)::nil) 1) ((Proof_certif 3 prime3) :: (Proof_certif 2 prime2) :: nil)). enc (refl_equal true). Qed.
Lemma
src
[ "From Coq Require Import List.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Pock." ]
src/Coqprime/examples/BasePrimes.v
prime229
prime233 : prime 233. Proof. apply (Pocklington_refl (Pock_certif 233 3 ((2,3)::nil) 12) ((Proof_certif 2 prime2) :: nil)). enc (refl_equal true). Qed.
Lemma
src
[ "From Coq Require Import List.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Pock." ]
src/Coqprime/examples/BasePrimes.v
prime233
prime239 : prime 239. Proof. apply (Pocklington_refl (Pock_certif 239 7 ((7, 1)::(2,1)::nil) 1) ((Proof_certif 7 prime7) :: (Proof_certif 2 prime2) :: nil)). enc (refl_equal true). Qed.
Lemma
src
[ "From Coq Require Import List.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Pock." ]
src/Coqprime/examples/BasePrimes.v
prime239
prime241 : prime 241. Proof. apply (Pocklington_refl (Pock_certif 241 7 ((2,4)::nil) 1) ((Proof_certif 2 prime2) :: nil)). enc (refl_equal true). Qed.
Lemma
src
[ "From Coq Require Import List.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Pock." ]
src/Coqprime/examples/BasePrimes.v
prime241
prime251 : prime 251. Proof. apply (Pocklington_refl (Pock_certif 251 6 ((5, 1)::(2,1)::nil) 4) ((Proof_certif 5 prime5) :: (Proof_certif 2 prime2) :: nil)). enc (refl_equal true). Qed.
Lemma
src
[ "From Coq Require Import List.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Pock." ]
src/Coqprime/examples/BasePrimes.v
prime251
prime257 : prime 257. Proof. apply (Pocklington_refl (Pock_certif 257 3 ((2,8)::nil) 1) ((Proof_certif 2 prime2) :: nil)). enc (refl_equal true). Qed.
Lemma
src
[ "From Coq Require Import List.", "From Coq Require Import ZArith.", "From Coqprime Require Import ZCAux.", "From Coqprime Require Import Pock." ]
src/Coqprime/examples/BasePrimes.v
prime257