unfolding dims_A'_pow[unfolded weight_space_dim_def] using card_rows_with_1 dims_Aw'_pow by simp_all
show "\<And>i j. i < r ^ N_half \<Longrightarrow> j < r ^ N_half \<Longrightarrow> polyfun {..<weight_space_dim} (\<lambda>f. witness_submatrix y f $$ (i, j))"
show "\<And>i j. i < r ^ N_half \<Longrightarrow> j < r ^ N_half \<Longrightarrow> polyfun {..<weight_space_dim} (\<lambda>f. witness_submatrix f $$ (i, j))"