This instance will be upgraded to Heptapod 0.31.0 (final) on 2022-05-24 at 14:00 UTC+2 (a few minutes of down time)

### Remove unnessecary argument from witness_submatrix

parent 71767e8d023f
 ... ... @@ -285,7 +285,7 @@ context deep_model_correct_params_y begin definition witness_submatrix where "witness_submatrix j f = submatrix (A' f) rows_with_1 rows_with_1" "witness_submatrix f = submatrix (A' f) rows_with_1 rows_with_1" lemma polyfun_tensor_deep_model: ... ... @@ -326,7 +326,7 @@ qed lemma polyfun_submatrix_deep_model: assumes "i < r ^ N_half" assumes "j < r ^ N_half" shows "polyfun {..f. witness_submatrix y f \$\$ (i,j))" shows "polyfun {..f. witness_submatrix f \$\$ (i,j))" unfolding witness_submatrix_def proof (rule polyfun_submatrix) have 1:"\f. remove_weights (insert_weights (deep_model_l rs) f) = deep_model_l rs" ... ... @@ -344,16 +344,16 @@ proof (rule polyfun_submatrix) qed lemma polyfun_det_deep_model: shows "polyfun {..f. det (witness_submatrix y f))" shows "polyfun {..f. det (witness_submatrix f))" proof (rule polyfun_det) fix f have "remove_weights (insert_weights (deep_model_l rs) f) = deep_model_l rs" using remove_insert_weights by metis show "witness_submatrix y f \ carrier\<^sub>m (r ^ N_half) (r ^ N_half)" show "witness_submatrix f \ carrier\<^sub>m (r ^ N_half) (r ^ N_half)" unfolding witness_submatrix_def apply (rule mat_carrierI) unfolding dim_submatrix[unfolded set_le_in] unfolding dims_A'_pow[unfolded weight_space_dim_def] using card_rows_with_1 dims_Aw'_pow by simp_all show "\i j. i < r ^ N_half \ j < r ^ N_half \ polyfun {..f. witness_submatrix y f \$\$ (i, j))" show "\i j. i < r ^ N_half \ j < r ^ N_half \ polyfun {..f. witness_submatrix f \$\$ (i, j))" using polyfun_submatrix_deep_model by blast qed ... ...
 ... ... @@ -15,7 +15,7 @@ and "\x. insertion x p \ 0 \ r ^ N_half \ cprank proof - assume assumption:"\p. p \ 0 \ vars p \ {.. (\x. insertion x p \ 0 \ r ^ N_half \ cprank (A x)) \ thesis" obtain p where p_def:"\x. insertion x p = Determinant.det (witness_submatrix y x)" and obtain p where p_def:"\x. insertion x p = Determinant.det (witness_submatrix x)" and vars_p:"vars p \ {.. 0" ... ... @@ -25,11 +25,11 @@ proof - have "\x. insertion x p \ 0 \ r ^ N_half \ cprank (A x)" proof - fix x assume "insertion x p \ 0" then have "Determinant.det (witness_submatrix y x) \ 0" using p_def by auto then have "Determinant.det (witness_submatrix x) \ 0" using p_def by auto have 0:"weight_space_dim \ length (map x [0.. mrank (A' x)" using vec_space.rank_gt_minor[OF mat_carrierI[OF dims_A'_pow, unfolded weight_space_dim_def] `Determinant.det (witness_submatrix y x) \ 0`[unfolded witness_submatrix_def]] `Determinant.det (witness_submatrix x) \ 0`[unfolded witness_submatrix_def]] card_rows_with_1[unfolded dims_Aw'_pow] by (metis (no_types, lifting) Collect_cong dims_A'_pow(1)) also have "... \ cprank (A x)" using matrix_rank_le_cp_rank A'_def by auto finally show "r ^ N_half \ cprank (A x)" . ... ...
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