reserve x,y for Real;
reserve z,z1,z2 for Complex;
reserve n for Element of NAT;

theorem Th48:
  cosh_C/.(x+y*<i>) = cosh.x*cos.y+sinh.x*sin.y*<i>
proof
  cosh_C/.(<i>*(y+(-x)*<i>)) = cos_C/.(y+(-x)*<i>) by Th18;
  hence thesis by Th45;
end;
