
theorem Th2:
  for i,n be Nat st i > 1 & i in Seg n holds i -' 1 in Seg n
proof
  let i,n be Nat;
  assume that
A1: i > 1 and
A2: i in Seg n;
  i - 1 > 1 - 1 by A1,XREAL_1:9;
  then i -' 1 > 0 by A1,XREAL_1:233;
  then
A3: i -' 1 >= 0 + 1 by NAT_1:13;
  i <= n by A2,FINSEQ_1:1;
  then i -' 1 <= n by NAT_D:44;
  hence thesis by A3,FINSEQ_1:1;
end;
