reserve N for Nat;
reserve n,m,n1,n2 for Nat;
reserve q,r,r1,r2 for Real;
reserve x,y for set;
reserve w,w1,w2,g,g1,g2 for Point of TOP-REAL N;
reserve seq,seq1,seq2,seq3,seq9 for Real_Sequence of N;

theorem
  seq is convergent & seq9 is convergent implies seq - seq9 is convergent
proof
  assume that
A1: seq is convergent and
A2: seq9 is convergent;
  -seq9 is convergent by A2,Th40;
  hence thesis by A1,Th36;
end;
