reserve i,j for Element of NAT,
  x,y,z for FinSequence of COMPLEX,
  c for Element of COMPLEX,
  R,R1,R2 for Element of i-tuples_on COMPLEX;
reserve C for Function of [:COMPLEX,COMPLEX:],COMPLEX;
reserve G for Function of [:REAL,REAL:],REAL;
reserve h for Function of COMPLEX,COMPLEX,
  g for Function of REAL,REAL;

theorem Th68:
  for a being Element of COMPLEX, x,y being FinSequence of COMPLEX
  st len x=len y holds |(x,a*y)| = (a*')*(|(x,y)|)
proof
  let a be Element of COMPLEX, x,y be FinSequence of COMPLEX;
  assume
A1: len x=len y;
  |(x,a*y)|=(|(a*y,x)|)*' by Th64
    .=(a*|(y,x)|)*' by A1,Th67
    .=(a*')*(|(y,x)|)*' by COMPLEX1:35
    .=(a*')*(|(x,y)|) by Th64;
  hence thesis;
end;
