let n, m, k be Nat; :: thesis: for K being Field
for M being Matrix of n,m,K holds ILine M,k,k = M
let K be Field; :: thesis: for M being Matrix of n,m,K holds ILine M,k,k = M
let M be Matrix of n,m,K; :: thesis: ILine M,k,k = M
A1: for i, j being Nat st [i,j] in Indices M holds
(ILine M,k,k) * i,j = M * i,j

proof

let i, j be Nat; :: thesis: ( [i,j] in Indices M implies (ILine M,k,k) * i,j = M * i,j )
assume [i,j] in Indices M ; :: thesis: (ILine M,k,k) * i,j = M * i,j
then A2: ( i in dom M & j in Seg (width M) ) by ZFMISC_1:106;
then ( i = k implies (ILine M,k,k) * i,j = M * k,j ) by Def1;
hence (ILine M,k,k) * i,j = M * i,j by A2, Def1; :: thesis: verum

end;

( len (ILine M,k,k) = len M & width (ILine M,k,k) = width M ) by Def1, Th1;
hence ILine M,k,k = M by A1, MATRIX_1:21; :: thesis: verum