reserve s for set,
  i,j for Nat,
  c,c1,c2,c3 for Complex,
  F,F1,F2 for complex-valued FinSequence,
  R,R1,R2 for i-element complex-valued FinSequence;

theorem
  R1 + R = R2 + R implies R1 = R2
proof
A0: R is i-element FinSequence of COMPLEX &
   R1 is i-element FinSequence of COMPLEX &
   R2 is i-element FinSequence of COMPLEX by FINSEQ_1:102;
  assume R1 + R = R2 + R; then
  R1 + (R + -R)= (R2 + R)+-R by A0,FINSEQOP:28; then
A1: R1 + (R + -R)= R2 + (R + -R) by A0,FINSEQOP:28;
  R + -R = i|->0c by A0,BINOP_2:1,FINSEQOP:73,SEQ_4:51,52; then
  R1 = R2 + (i|->0c) by A0,A1,BINOP_2:1,FINSEQOP:56;
  hence thesis by A0,BINOP_2:1,FINSEQOP:56;
end;
