reserve n for Element of NAT,
  i for Integer,
  a, b, r for Real,
  x for Point of TOP-REAL n;

theorem Th1:
  sin(a*r+b) = (sin*AffineMap(a,b)).r
proof
A1: r in REAL by XREAL_0:def 1;
  thus sin(a*r+b) = sin.(a*r+b) by SIN_COS:def 17
    .= sin.(AffineMap(a,b).r) by FCONT_1:def 4
    .= (sin*AffineMap(a,b)).r by A1,FUNCT_2:15;
end;
