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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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24
projects/lib/gmp_proof_manual.v
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@ -871,7 +871,27 @@ Proof.
Exists (val_a_prefix_2 + (Znth i l_a_2 0) * (UINT_MOD ^ i)).
Exists l_b_2 l_a_2.
entailer!.
+ admit.
+ assert ( (val_a_prefix_2 + Znth i l_a_2 0 * 4294967296 ^ i +(val_b_prefix_2 + Znth i l_b_2 0 * 4294967296 ^ i)) = (val_a_prefix_2 + val_b_prefix_2) + Znth i l_a_2 0 * 4294967296 ^ i + Znth i l_b_2 0 * 4294967296 ^ i).
{
lia.
}
rewrite H37; clear H37.
rewrite <- H19.
assert ( (Znth i l_a_2 0) + (Znth i l_b_2 0) + cy = partial_result_2 + UINT_MOD). {
unfold unsigned_last_nbits in H4, H3.
assert (2 ^ 32 = 4294967296). { nia. }
rewrite H37 in H4, H3; clear H37.
apply Z_mod_3add_carry10; try lia; try tauto;
try unfold list_store_Z_compact in H13, H14;
try apply list_within_bound_Znth;
try lia;
try tauto.
}
assert ( partial_result_2 * 4294967296 ^ i + (1 + 0) * 4294967296 ^ (i + 1) = cy * 4294967296 ^ i + Znth i l_a_2 0 * 4294967296 ^ i + Znth i l_b_2 0 * 4294967296 ^ i). {
rewrite <- Z.mul_add_distr_r.
rewrite (Zpow_add_1 4294967296 i); try lia.
}
lia.
+ pose proof (Zlength_app l_r_prefix_2 (partial_result_2 :: nil)).
assert (Zlength (partial_result_2 :: nil) = 1). {
unfold Zlength.
@ -909,7 +929,7 @@ Proof.
tauto.
- pose proof (Zlength_sublist0 i l_r_prefix_2).
lia.
Admitted.
Qed.
Lemma proof_of_mpn_add_n_entail_wit_3_2 : mpn_add_n_entail_wit_3_2.
Proof. Admitted.