reserve s for set,
  i,j for natural Number,
  k for Nat,
  x,x1,x2,x3 for Real,
  r,r1,r2,r3,r4 for Real,
  F,F1,F2,F3 for real-valued FinSequence,
  R,R1,R2 for Element of i-tuples_on REAL;

theorem
  R1 = R1 + R - R
proof
  thus R1 = R1 + (i|->(0 qua Real)) by BINOP_2:2,FINSEQOP:56
    .= R1 + (R - R) by Th8,Th9,BINOP_2:2,FINSEQOP:73
    .= R1 + R - R by RFUNCT_1:23;
end;
