proposition: Lemma switch_row_other_row' {m n} (r1 r2 : ⟦ m ⟧%stn) (mat : Matrix R m n) : ∏ (i : ⟦ m ⟧%stn), i ≠ r1 -> i ≠ r2 -> (switch_row r1 r2 mat) i = mat i.
proof: Proof. intros i i_ne_r1 i_ne_r2. apply funextfun; intros j. apply switch_row_other_row; assumption. Defined.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.Combinatorics.StandardFiniteSets UniMath.Combinatorics.Vectors UniMath.Algebra.Matrix UniMath.Algebra.RigsAndRings UniMath.Algebra.IteratedBinaryOperations UniMath.Algebra.Domains_and_Fields UniMath.Algebra.GaussianElimination.Auxiliary UniMath.Algebra.GaussianElimination.Vectors UniMath.Algebra.GaussianElimination.Matrices