reserve m,k,j,j1,i,i1,i2,n for Nat,
  r,s for Real,
  C for compact non vertical non horizontal Subset of TOP-REAL 2,
  G for Go-board,
  p for Point of TOP-REAL 2;

theorem Th27:
  for f being FinSequence of TOP-REAL 2, M being Go-board holds f
  is_sequence_on M implies mid(f,i1,i2) is_sequence_on M
proof
  let f be FinSequence of TOP-REAL 2, M be Go-board;
  assume
A1: f is_sequence_on M;
  per cases;
  suppose
A2: i1<=i2;
A3: f/^(i1-'1) is_sequence_on M by A1,JORDAN8:2;
    mid(f,i1,i2) = (f/^(i1-'1))|(i2-'i1+1) by A2,FINSEQ_6:def 3;
    hence thesis by A3,GOBOARD1:22;
  end;
  suppose
A4: i1 > i2;
    f/^(i2-'1) is_sequence_on M by A1,JORDAN8:2;
    then
A5: (f/^(i2-'1))|(i1-'i2+1) is_sequence_on M by GOBOARD1:22;
    mid(f,i1,i2) = Rev ((f/^(i2-'1))|(i1-'i2+1)) by A4,FINSEQ_6:def 3;
    hence thesis by A5,JORDAN9:5;
  end;
end;
