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 Th62:
  for x1,x2,y1,y2 being FinSequence of COMPLEX st len x1=len x2 &
  len x2=len y1 & len y1=len y2 holds
  |(x1+x2, y1+y2)| = |(x1, y1)| + |(x1, y2)| + |(x2, y1)| + |(x2, y2)|
proof
  let x1,x2,y1,y2 be FinSequence of COMPLEX;
  assume that
A1: len x1=len x2 and
A2: len x2=len y1 and
A3: len y1=len y2;
  |(x1+x2, y2)| = |(x1, y2)| + |(x2, y2)| by A1,A2,A3,Th55;
  then
A4: |(x1+x2, y1)| + |(x1+x2, y2)| = (|(x1, y1)|+|(x2, y1)|) + (|(x1, y2)| +
  |(x2, y2)|) by A1,A2,Th55;
  len (x1+x2)=len x1 by A1,Th6;
  hence thesis by A1,A2,A3,A4,Th60;
end;
