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

theorem
  M1 is Self_Reversible Idempotent implies M1=1.(K,n)
proof
  assume
A1: M1 is Self_Reversible Idempotent;
  then M1 is invertible;
  then M1~ is_reverse_of M1 by MATRIX_6:def 4;
  then 1.(K,n)=M1*M1~ by MATRIX_6:def 2
    .=M1*M1 by A1;
  hence thesis by A1;
end;
