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feat(cmp4): modied certain annotations for mpn_cmp and proved correctness of mpn_cmp4.

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xiaoh105
2025-06-12 12:37:01 +08:00
parent 36204b8877
commit f7432dca84
7 changed files with 788 additions and 166 deletions
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72
projects/lib/gmp_proof_manual.v
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@ -198,9 +198,9 @@ Lemma proof_of_mpn_cmp_return_wit_1_1 : mpn_cmp_return_wit_1_1.
Proof.
pre_process.
entailer!.
repeat rewrite <-derivable1_orp_intros1.
Left; Left.
entailer!.
+ unfold mpd_store_Z.
+ unfold mpd_store_Z_compact.
Exists l1 l2.
unfold mpd_store_list.
entailer!.
@ -208,7 +208,7 @@ Proof.
entailer!.
+ assert (Znth n l1 0 < Znth n l2 0). { lia. }
clear H H0.
apply (list_store_Z_cmp l1 l2 val1 val2 n ltac:(lia) ltac:(lia) H4 H5).
apply (list_store_Z_compact_cmp l1 l2 val1 val2 n ltac:(lia) ltac:(lia) H4 H5).
- rewrite <-H6, <-H7.
tauto.
- lia.
@ -217,13 +217,13 @@ Qed.
Lemma proof_of_mpn_cmp_return_wit_1_2 : mpn_cmp_return_wit_1_2.
Proof.
pre_process.
rewrite <-derivable1_orp_intros2.
Right.
entailer!.
+ unfold mpd_store_Z, mpd_store_list.
+ unfold mpd_store_Z_compact, mpd_store_list.
Exists l1 l2.
rewrite <-H6, <-H7.
entailer!.
+ pose proof (list_store_Z_cmp l2 l1 val2 val1 n ltac:(lia) ltac:(lia) H5 H4).
+ pose proof (list_store_Z_compact_cmp l2 l1 val2 val1 n ltac:(lia) ltac:(lia) H5 H4).
rewrite <-H6, <-H7 in H18.
rewrite H8 in H18.
specialize (H18 ltac:(reflexivity) ltac:(lia)).
@ -233,11 +233,67 @@ Qed.
Lemma proof_of_mpn_cmp_which_implies_wit_1 : mpn_cmp_which_implies_wit_1.
Proof.
pre_process.
unfold mpd_store_Z.
unfold mpd_store_Z_compact.
Intros l1 l2.
Exists l2 l1.
unfold mpd_store_list.
entailer!.
rewrite <-H4, <-H6.
rewrite <-H0, <-H2.
entailer!.
Qed.
Lemma proof_of_mpn_cmp4_return_wit_1_1 : mpn_cmp4_return_wit_1_1.
Proof.
pre_process.
Right.
unfold mpd_store_Z_compact.
Intros l1 l2.
Exists l1 l2.
entailer!.
pose proof (list_store_Z_cmp_length l2 l1 val2 val1 ltac:(lia) H9 H7).
lia.
Qed.
Lemma proof_of_mpn_cmp4_return_wit_1_2 : mpn_cmp4_return_wit_1_2.
Proof.
pre_process.
Left; Left.
unfold mpd_store_Z_compact.
entailer!.
Intros l1 l2.
Exists l1 l2.
entailer!.
pose proof (list_store_Z_cmp_length l1 l2 val1 val2 ltac:(lia) H7 H9).
lia.
Qed.
Lemma proof_of_mpn_cmp4_return_wit_2_1 : mpn_cmp4_return_wit_2_1.
Proof.
pre_process.
Right.
unfold mpd_store_Z_compact.
Intros l1 l2.
Exists l1 l2.
entailer!.
Qed.
Lemma proof_of_mpn_cmp4_return_wit_2_2 : mpn_cmp4_return_wit_2_2.
Proof.
pre_process.
Left; Right.
unfold mpd_store_Z_compact.
Intros l1 l2.
Exists l1 l2.
entailer!.
Qed.
Lemma proof_of_mpn_cmp4_return_wit_2_3 : mpn_cmp4_return_wit_2_3.
Proof.
pre_process.
Left; Left.
unfold mpd_store_Z_compact.
Intros l1 l2.
Exists l1 l2.
entailer!.
Qed.