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 Th7:
  compreal is_an_inverseOp_wrt addreal
proof
  let x be Element of REAL;
  thus addreal.(x,compreal.x) = x+compreal.x by BINOP_2:def 9
    .= x+-x by BINOP_2:def 7
    .= the_unity_wrt addreal by BINOP_2:2;
  thus addreal.(compreal.x,x) = compreal.x+x by BINOP_2:def 9
    .= -x+x by BINOP_2:def 7
    .= the_unity_wrt addreal by BINOP_2:2;
end;
