reserve i,j,k,n for Nat;
reserve D for non empty set,
  p for Element of D,
  f,g for FinSequence of D;

theorem Th70:
  rng Ins(f,n,p) = {p} \/ rng f
proof
  thus rng Ins(f,n,p) = rng((f|n)^<*p*>) \/ rng(f/^n) by FINSEQ_1:31
    .= rng(f|n) \/ rng<*p*> \/ rng(f/^n) by FINSEQ_1:31
    .= rng(f|n) \/ rng(f/^n) \/ rng<*p*> by XBOOLE_1:4
    .= rng((f|n)^(f/^n)) \/ rng<*p*> by FINSEQ_1:31
    .= rng<*p*> \/ rng f by RFINSEQ:8
    .= {p} \/ rng f by FINSEQ_1:38;
end;
