reserve x,y,z for object,
  i,j,n,m for Nat,
  D for non empty set,
  s,t for FinSequence,
  a,a1,a2,b1,b2,d for Element of D,
  p, p1,p2,q,r for FinSequence of D;
reserve M,M1,M2 for Matrix of D;

theorem
  for M1 being Matrix of n,D holds for i,j st [i,j] in Indices M1 holds
  [j,i] in Indices M1
proof
  let M1 be Matrix of n,D;
  let i,j;
  assume [i,j] in Indices M1;
  then [i,j] in [:Seg n,Seg n:] by Th24;
  then
A1: j in Seg n & i in Seg n by ZFMISC_1:87;
  Indices M1 =[:Seg n,Seg n:] by Th24;
  hence thesis by A1,ZFMISC_1:87;
end;
