reserve a,b for Complex;
reserve V,X,Y for ComplexLinearSpace;
reserve u,u1,u2,v,v1,v2 for VECTOR of V;
reserve z,z1,z2 for Complex;
reserve V1,V2,V3 for Subset of V;
reserve W,W1,W2 for Subspace of V;
reserve x for set;
reserve w,w1,w2 for VECTOR of W;

theorem Th34:
  w = v implies - v = - w
proof
  assume
A1: w = v;
  - v = (- 1r) * v & - w = (- 1r) * w by Th3;
  hence thesis by A1,Th33;
end;
