reserve n,i,j,k,l for Nat;
reserve D for non empty set;
reserve c,d for Element of D;
reserve p,q,q9,r for FinSequence of D;

theorem
  l in Seg(n)\{i} & i=j+1 implies 1<=l & l<=j or i+1<=l & l<=n
proof
  assume that
A1: l in Seg(n)\{i} and
A2: i=j+1;
A3: i+1 = j+2 by A2;
  l in Seg(n) & l<>i by A1,ZFMISC_1:56;
  hence thesis by A2,A3,Th4,FINSEQ_1:1;
end;
