reserve q,th,r for Real,
  a,b,p for Real,
  w,z for Complex,
  k,l,m,n,n1,n2 for Nat,
  seq,seq1,seq2,cq1 for Complex_Sequence,
  rseq,rseq1,rseq2 for Real_Sequence,
  rr for set,
  hy1 for 0-convergent non-zero Real_Sequence;
reserve d for Real;
reserve th,th1,th2 for Real;

theorem
  sin(th+2 * PI) = sin(th) & cos(th+2 * PI) = cos(th) &
  sin(PI/2-th) = cos(th) & cos(PI/2-th) = sin(th) & sin(PI/2+th) = cos(th) &
  cos(PI/2+th) = -sin(th) & sin(PI+th) = -sin(th) &
  cos(PI+th) = -cos(th) by Th77;
