reserve n,k,k1,m,m1,n1,n2,l for Nat;
reserve r,r1,r2,p,p1,g,g1,g2,s,s1,s2,t for Real;
reserve seq,seq1,seq2 for Real_Sequence;
reserve Nseq for increasing sequence of NAT;
reserve x for set;
reserve X,Y for Subset of REAL;
reserve k,n for Nat,
  r,r9,r1,r2 for Real,
  c,c9,c1,c2,c3 for Element of COMPLEX;
reserve z,z1,z2 for FinSequence of COMPLEX;
reserve x,z,z1,z2,z3 for Element of COMPLEX n,
  A,B for Subset of COMPLEX n;

theorem Th65:
  -(z1 + z2) = -z1 + -z2
proof
  (z1 + z2) + (-z1 + -z2) = z2 + z1 + -z1 + -z2 by FINSEQOP:28
    .= z2 + (z1 + -z1) + -z2 by FINSEQOP:28
    .= z2 + 0c n + -z2 by Th51,Th52,BINOP_2:1,FINSEQOP:73
    .= z2 + -z2 by BINOP_2:1,FINSEQOP:56
    .= 0c n by Th51,Th52,BINOP_2:1,FINSEQOP:73;
  hence thesis by Th51,Th52,BINOP_2:1,FINSEQOP:74;
end;
