fact: Definition is_leading_entry {n : nat} (v : Vector R n) (i_1 : ⟦ n ⟧%stn) := (v i_1 != 0%ring) × (∏ i_2 : ⟦ n ⟧%stn, i_2 < i_1 -> (v i_2) = 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