ZYM/MiniGmp-Verification
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Merge remote-tracking branch 'origin/main' into mpz_sgn

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xiaoh105
2025-06-22 19:14:56 +08:00
parent 3a102d0d65 4c13bd6648
commit 77ccdd3e50
7 changed files with 3124 additions and 91 deletions
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41
projects/lib/GmpNumber.v
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@ -89,9 +89,9 @@ Proof.
reflexivity.
Qed.
Lemma list_store_Z_compact_reverse_injection: forall l1 l2 n1 n2,
list_store_Z_compact l1 n1 ->
list_store_Z_compact l2 n2 ->
Lemma list_store_Z_reverse_injection: forall l1 l2 n1 n2,
list_store_Z l1 n1 ->
list_store_Z l2 n2 ->
n1 = n2 -> l1 = l2.
Proof. Admitted.
@ -282,6 +282,41 @@ Proof.
pose proof (Zlength_nonneg l1); lia.
Qed.
Lemma list_store_Z_list_append: forall (l: list Z) (i: Z) (val_prefix: Z) (val_full: Z),
0 <= i < Zlength l ->
list_store_Z l val_full ->
list_store_Z (sublist 0 i l) val_prefix ->
list_store_Z (sublist 0 (i+1) l) (val_prefix + Znth i l 0 * UINT_MOD ^ i).
Proof.
intros.
assert ((sublist 0 (i + 1) l) = ((sublist 0 i l) ++ ((Znth i l 0) :: nil)))%list. {
pose proof (sublist_split 0 (i+1) i l).
pose proof (sublist_single i l 0).
rewrite <-H3; try rewrite <- Zlength_correct.
apply H2; try rewrite <- Zlength_correct.
lia. lia. lia.
}
rewrite H2.
pose proof (list_store_Z_concat (sublist 0 i l) (Znth i l 0 :: nil) (val_prefix) (Znth i l 0)).
assert (Zlength (sublist 0 i l) = i). {
rewrite Zlength_sublist0.
lia.
lia.
}
rewrite H4 in H3.
apply H3.
tauto.
unfold list_store_Z.
simpl.
split.
reflexivity.
split; try tauto.
apply list_within_bound_Znth.
lia.
unfold list_store_Z in H0.
tauto.
Qed.
Lemma list_store_Z_split: forall (l1 l2: list Z) (n: Z),
list_store_Z (l1 ++ l2) n ->
list_store_Z l1 (n mod UINT_MOD ^ (Zlength l1)) /\