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

theorem Th16:
  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) = g
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;
A3: 1 <= len g by NAT_1:14;
A4: 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) = <*g/.1*>^(f^'g |-- g/.1) by A2,FINSEQ_6:41
    .= <*g/.1*>^(2, len g)-cut g by A1,A4,Th5
    .= <*g.1*>^(2, len g)-cut g by A3,FINSEQ_4:15
    .= ((1,1)-cut g)^(1+1, len g)-cut g by A3,FINSEQ_6:132
    .= g by FINSEQ_6:135,NAT_1:14;
end;
