reserve i,j for Nat;

theorem Th56:
  for a being Real, M being (Matrix of REAL), i being Nat st 1<=i
  & i<=width M holds Col(a*M,i)=a*Col(M,i)
proof
  let a be Real, M be Matrix of REAL;
  reconsider ea=a as Element of F_Real by XREAL_0:def 1;
  let i be Nat;
  assume
A1: 1<=i & i<=width M;
  Col(a*M,i)=Col(MXF2MXR (ea*(MXR2MXF M)),i) by Def7
    .=ea*Col(MXR2MXF M,i) by A1,Th19;
  hence thesis by Th17;
end;
