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finish proof_of_mpn_add_n_entail_wit_3_1

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ZhuangYumin
2025-06-22 07:25:46 +00:00
parent 6167816613
commit 0fdf4fc328
2 changed files with 50 additions and 2 deletions
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projects/lib/GmpAux.v
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@ -33,6 +33,34 @@ Lemma Z_mod_add_uncarry: forall (a b m: Z),
a + b = (a + b) mod m.
Proof. Admitted.
Lemma Z_mod_3add_carry10: forall (a b c m: Z),
m > 0 -> 0 <= a < m -> 0 <= b < m -> 0 <= c < m ->
(a + c) mod m < c ->
((a + c) mod m + b) mod m >= b ->
a + b + c = ((a + c) mod m + b) mod m + m.
Proof. Admitted.
Lemma Z_mod_3add_carry01: forall (a b c m: Z),
m > 0 -> 0 <= a < m -> 0 <= b < m -> 0 <= c < m ->
(a + c) mod m >= c ->
((a + c) mod m + b) mod m < b ->
a + b + c = ((a + c) mod m + b) mod m + m.
Proof. Admitted.
Lemma Z_mod_3add_carry11: forall (a b c m: Z),
m > 0 -> 0 <= a < m -> 0 <= b < m -> 0 <= c < m ->
(a + c) mod m < c ->
((a + c) mod m + b) mod m < b ->
a + b + c = ((a + c) mod m + b) mod m + m.
Proof. Admitted.
Lemma Z_mod_3add_carry00: forall (a b c m: Z),
m > 0 -> 0 <= a < m -> 0 <= b < m -> 0 <= c < m ->
(a + c) mod m >= c ->
((a + c) mod m + b) mod m >= b ->
a + b + c = ((a + c) mod m + b) mod m.
Proof. Admitted.
Lemma Z_of_nat_succ: forall (n: nat),
Z.of_nat (S n) = Z.of_nat n + 1.
Proof. lia. Qed.