reserve x,x0, r, s, h for Real,

  n for Element of NAT,
  rr, y for set,
  Z for open Subset of REAL,

  f, f1, f2 for PartFunc of REAL,REAL;

theorem Th17:
  tan.(-PI/4) = -1 & tan(-PI/4) = -1
proof
  cos.(PI/4) <> 0 by Lm8,COMPTRIG:11;
  then
A1: sin.(PI/4)/cos.(PI/4) = 1 by SIN_COS:73,XCMPLX_1:60;
  tan.(-PI/4) = sin.(-PI/4)/(cos.(-PI/4)) by Lm7,Th1,RFUNCT_1:def 1
    .= (-sin.(PI/4))/cos.(-PI/4) by SIN_COS:30
    .= (-sin.(PI/4))/cos.(PI/4) by SIN_COS:30
    .= -1 by A1;
  hence thesis by Lm7,Th13;
end;
