ZYM/MiniGmp-Verification
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ready to prove the correctness of 3-carry

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ZhuangYumin
2025-06-22 06:58:57 +00:00
parent 1e3c1ea7ec
commit 6167816613
2 changed files with 111 additions and 1 deletions
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projects/lib/GmpNumber.v
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@ -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_compact 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_compact 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)) /\