fact: Definition select_pivot_row_coprod {m n : nat} (mat : Matrix F m n) (row_sep : ⟦ m ⟧%stn) (k : ⟦ n ⟧%stn) : coprod ((∑ i: ⟦ m ⟧%stn, row_sep ≤ i × ((mat i k) != 0%ring))) (∏ i : ⟦ m ⟧%stn, row_sep ≤ i -> mat i k = 0%ring).
imports: UniMath.Foundations.PartA UniMath.Foundations.NaturalNumbers UniMath.MoreFoundations.PartA UniMath.MoreFoundations.Nat UniMath.MoreFoundations.Tactics UniMath.Combinatorics.StandardFiniteSets UniMath.Combinatorics.FiniteSequences UniMath.Combinatorics.Vectors UniMath.Combinatorics.Maybe UniMath.Algebra.BinaryOperations UniMath.Algebra.IteratedBinaryOperations UniMath.Algebra.RigsAndRings UniMath.Algebra.Matrix UniMath.Algebra.Domains_and_Fields UniMath.Algebra.GaussianElimination.Auxiliary UniMath.Algebra.GaussianElimination.Vectors UniMath.Algebra.GaussianElimination.Matrices UniMath.Algebra.GaussianElimination.RowOps