reserve i,n for Nat,
  K for Field,
  M1,M2,M3,M4 for Matrix of n,K;

theorem
  M1 is Self_Reversible symmetric implies M1 is Orthogonal
proof
  assume
A1: M1 is Self_Reversible symmetric;
  then
A2: M1=M1@ by MATRIX_6:def 5;
  M1 is invertible & M1=M1~ by A1;
  hence thesis by A2,MATRIX_6:def 7;
end;
