theorem
  -1 <= r & r <= 1 & arctan r = PI/4 implies r = 1
proof
  assume that
A1: -1 <= r and
A2: r <= 1 and
A3: arctan r = PI/4;
  thus r = tan(PI/4) by A1,A2,A3,Th51
    .= tan.(PI/4) by Lm8,Th13
    .= 1 by SIN_COS:def 28;
end;
