reserve G for Go-board,
  i,j,k,m,n for Nat;

theorem Th17:
  for D being non empty set for f,g being non empty FinSequence of
  D st g/.1..f = len f holds (f^'g-:g/.1) = f
proof
  let D be non empty set;
  let f,g be non empty FinSequence of D such that
A1: g/.1..f = len f;
A2: g/.1 in rng f by A1,Th4;
  g/.1 in rng f by A1,Th4;
  then
A3: g/.1 = f.len f by A1,FINSEQ_4:19;
A4: 1 <= len f by NAT_1:14;
A5: len f -' 1 + 1 = len f by NAT_1:14,XREAL_1:235;
A6: f^'g = f^(2, len g)-cut g by FINSEQ_6:def 5;
  then rng f c= rng(f^'g) by FINSEQ_1:29;
  hence (f^'g-:g/.1) = (f^'g -| g/.1)^<*g/.1*> by A2,FINSEQ_6:40
    .= ((1, len f -' 1)-cut f)^<*g/.1*> by A1,A6,Th15
    .= ((1, len f -' 1)-cut f)^((len f,len f)-cut f) by A4,A3,FINSEQ_6:132
    .= f by A5,FINSEQ_6:135,NAT_D:44;
end;
