feat(mpz_clear & mpz_realloc): Proved correctness of mpz_clear and mpz_realloc
This commit is contained in:
xiaoh105
297
projects/lib/gmp_proof_manual.v
Normal file → Executable file
297
projects/lib/gmp_proof_manual.v
Normal file → Executable file
@ -410,4 +410,299 @@ Proof.
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entailer!.
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+ rewrite sublist_self; try lia.
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tauto.
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Qed.
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Qed.
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Lemma proof_of_mpz_clear_return_wit_1_1 : mpz_clear_return_wit_1_1.
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Proof.
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pre_process.
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Exists ptr_2 cap_2 size_2.
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entailer!.
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unfold mpd_store_Z_compact.
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Intros data.
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unfold mpd_store_list.
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subst.
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entailer!.
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Qed.
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Lemma proof_of_mpz_clear_return_wit_1_2 : mpz_clear_return_wit_1_2.
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Proof.
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pre_process.
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Exists ptr_2 cap_2 size_2.
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entailer!.
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unfold mpd_store_Z_compact.
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Intros data.
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unfold mpd_store_list.
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entailer!.
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assert (size_2 = 0). {
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pose proof (Zlength_nonneg data).
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lia.
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}
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rewrite H6 in *.
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rewrite <-H3 in *.
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unfold store_uint_array, store_undef_uint_array_rec.
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unfold store_array.
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assert (cap_2 - 0 = 0). { lia. }
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rewrite H7; clear H7.
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pose proof (Zlength_nil_inv data ltac:(lia)).
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rewrite H7 in *; clear H7.
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simpl.
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entailer!.
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Qed.
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Lemma proof_of_mpz_clear_return_wit_1_3 : mpz_clear_return_wit_1_3.
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Proof.
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pre_process.
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Exists ptr_2 cap_2 size_2.
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entailer!.
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Qed.
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Lemma proof_of_mpz_clear_return_wit_1_4 : mpz_clear_return_wit_1_4.
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Proof.
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pre_process.
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Exists ptr_2 cap_2 size_2.
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entailer!.
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Qed.
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Lemma proof_of_mpz_clear_which_implies_wit_1 : mpz_clear_which_implies_wit_1.
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Proof.
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pre_process.
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unfold store_Z.
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Intros ptr cap size.
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entailer!.
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rewrite orp_sepcon_left.
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Split.
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+ Right.
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Exists ptr cap size.
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entailer!.
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+ Left.
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Exists ptr cap size.
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entailer!.
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Qed.
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Lemma proof_of_mpz_realloc_return_wit_1_1 : mpz_realloc_return_wit_1_1.
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Proof.
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pre_process.
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Right.
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Exists retval_3 retval_2.
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entailer!.
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unfold Zmax in *.
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pose proof (Z.le_max_l size_pre 1).
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lia.
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Qed.
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Lemma proof_of_mpz_realloc_return_wit_1_2 : mpz_realloc_return_wit_1_2.
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Proof.
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pre_process.
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Left.
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Exists retval_3 retval_2.
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entailer!.
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unfold Zmax in *.
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pose proof (Z.le_max_l size_pre 1).
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lia.
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Qed.
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Lemma proof_of_mpz_realloc_return_wit_1_3 : mpz_realloc_return_wit_1_3.
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Proof.
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pre_process.
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Right.
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Exists retval_3 retval_2.
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entailer!.
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+ subst.
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unfold mpd_store_Z_compact.
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Intros data.
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Exists data.
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unfold mpd_store_list, store_undef_uint_array_rec.
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entailer!.
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- assert (Zlength data = 0). {
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pose proof (Zlength_nonneg data).
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lia.
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}
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rewrite H8 in *.
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simpl.
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entailer!.
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pose proof (Zlength_nil_inv data H8).
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repeat subst.
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unfold store_uint_array, store_array; simpl; entailer!.
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unfold store_undef_uint_array, store_undef_array.
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rewrite Z.sub_0_r.
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reflexivity.
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- unfold Zmax in *.
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assert (size_pre < 1 \/ size_pre >= 1). { lia. }
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destruct H8.
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* rewrite (Z.max_r size_pre 1 ltac:(lia)); lia.
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* rewrite (Z.max_l size_pre 1 ltac:(lia)); lia.
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+ pose proof (Z.le_max_l size_pre 1).
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unfold Zmax in *.
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lia.
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Qed.
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Lemma proof_of_mpz_realloc_return_wit_1_4 : mpz_realloc_return_wit_1_4.
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Proof.
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pre_process.
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Left.
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Exists retval_3 retval_2.
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entailer!.
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+ subst.
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unfold mpd_store_Z_compact, mpd_store_list.
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Intros data.
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Exists data.
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assert (Zlength data = 0). {
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pose proof (Zlength_nonneg data).
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lia.
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}
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rewrite H8 in *; clear H2.
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pose proof (Zlength_nil_inv data H8).
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rewrite H2 in *; clear H2 H8.
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unfold store_uint_array, store_array.
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simpl.
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entailer!.
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+ pose proof (Z.le_max_l size_pre 1).
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unfold Zmax in *.
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lia.
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Qed.
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Lemma proof_of_mpz_realloc_return_wit_1_5 : mpz_realloc_return_wit_1_5.
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Proof.
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pre_process.
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Left.
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Exists retval_3 retval_2.
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entailer!.
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+ subst.
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unfold mpd_store_Z_compact, mpd_store_list.
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Intros data.
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Exists data.
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unfold store_uint_array, store_array.
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simpl.
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entailer!.
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+ pose proof (Z.le_max_l size_pre 1).
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unfold Zmax in *.
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lia.
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Qed.
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Lemma proof_of_mpz_realloc_return_wit_1_6 : mpz_realloc_return_wit_1_6.
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Proof.
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pre_process.
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Right.
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Exists retval_3 retval_2.
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subst.
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entailer!.
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+ unfold mpd_store_Z_compact, mpd_store_list.
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Intros data; Exists data.
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unfold store_uint_array, store_array.
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assert (Zlength data = 0). {
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pose proof (Zlength_nonneg data).
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lia.
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}
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rewrite H8 in *; clear H2.
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pose proof (Zlength_nil_inv data H8).
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rewrite H2 in *; clear H2 H8.
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unfold store_undef_uint_array, store_undef_uint_array_rec, store_undef_array.
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subst.
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simpl.
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entailer!.
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- rewrite Z.sub_0_r.
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entailer!.
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- pose proof (Z.le_max_r size_pre 1).
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simpl in H.
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unfold Zmax in *.
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lia.
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+ unfold Zmax in *.
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pose proof (Z.le_max_l size_pre 1).
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lia.
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Qed.
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Lemma proof_of_mpz_realloc_return_wit_1_7 : mpz_realloc_return_wit_1_7.
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Proof.
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pre_process.
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Left.
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Exists retval_3 retval_2.
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subst.
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unfold Zmax in *.
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rewrite (Z.abs_neq old ltac:(lia)) in H.
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pose proof (Z.le_max_l size_pre 1).
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unfold mpd_store_Z_compact.
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Intros data; entailer!.
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unfold mpd_store_list.
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entailer!.
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Qed.
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Lemma proof_of_mpz_realloc_return_wit_1_8 : mpz_realloc_return_wit_1_8.
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Proof.
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pre_process.
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Right.
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Exists retval_3 retval_2.
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subst.
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unfold Zmax in *.
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rewrite (Z.abs_eq old ltac:(lia)) in H.
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pose proof (Z.le_max_l size_pre 1).
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unfold mpd_store_Z_compact.
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Intros data; entailer!.
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unfold mpd_store_list.
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entailer!.
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Qed.
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Lemma proof_of_mpz_realloc_partial_solve_wit_3_pure : mpz_realloc_partial_solve_wit_3_pure.
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Proof.
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pre_process.
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unfold Zmax in *.
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pose proof (Z.le_max_l size_pre 1).
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entailer!.
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Qed.
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Lemma proof_of_mpz_realloc_partial_solve_wit_4_pure : mpz_realloc_partial_solve_wit_4_pure.
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Proof.
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pre_process.
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unfold Zmax in *.
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pose proof (Z.le_max_l size_pre 1).
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entailer!.
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Qed.
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Lemma proof_of_mpz_realloc_partial_solve_wit_5_pure : mpz_realloc_partial_solve_wit_5_pure.
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Proof.
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pre_process.
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unfold Zmax in *.
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pose proof (Z.le_max_l size_pre 1).
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entailer!.
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Qed.
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Lemma proof_of_mpz_realloc_partial_solve_wit_6_pure : mpz_realloc_partial_solve_wit_6_pure.
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Proof.
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pre_process.
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unfold Zmax in *.
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pose proof (Z.le_max_l size_pre 1).
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entailer!.
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Qed.
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Lemma proof_of_mpz_realloc_partial_solve_wit_7_pure : mpz_realloc_partial_solve_wit_7_pure.
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Proof.
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pre_process.
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unfold mpd_store_Z_compact, mpd_store_list.
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Intros data.
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entailer!.
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Qed.
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Lemma proof_of_mpz_realloc_partial_solve_wit_8_pure : mpz_realloc_partial_solve_wit_8_pure.
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Proof.
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pre_process.
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unfold mpd_store_Z_compact, mpd_store_list.
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Intros data.
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entailer!.
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Qed.
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Lemma proof_of_mpz_realloc_partial_solve_wit_9_pure : mpz_realloc_partial_solve_wit_9_pure.
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Proof.
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pre_process.
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unfold mpd_store_Z_compact, mpd_store_list.
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Intros data.
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entailer!.
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Qed.
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Lemma proof_of_mpz_realloc_partial_solve_wit_10_pure : mpz_realloc_partial_solve_wit_10_pure.
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Proof.
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pre_process.
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unfold mpd_store_Z_compact, mpd_store_list.
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Intros data.
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entailer!.
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Qed.
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