
theorem Th3:
  for D being set,p being FinSequence of D,i,j being Element of NAT
  st i in dom p & j in dom p holds len Del(p,i,j) = 0 implies i=1 & j=len p
proof
  let D be set;
  let p be FinSequence of D;
  let i,j be Element of NAT;
  assume that
A1: i in dom p and
A2: j in dom p and
A3: len Del(p,i,j) = 0;
A4: 1 <= i by A1,FINSEQ_3:25;
  j <= len p by A2,FINSEQ_3:25;
  then
A5: len p - j >= 0 by XREAL_1:48;
A6: len p - j + i - 1 = 0 by A1,A2,A3,Th2;
  then len p - j = 1 - i;
  then 1 >= i by A5,XREAL_1:49;
  hence i=1 by A4,XXREAL_0:1;
  hence thesis by A6;
end;
