
theorem
  for n being object holds (seq_id Zeroseq).n = 0
  proof
    set f = seq_id Zeroseq;
    let n be object;
    per cases;
    suppose
A1:   n in dom f;
      dom f = NAT by FUNCT_2:def 1;
      hence thesis by A1,FUNCOP_1:7;
    end;
    suppose not n in dom f;
      hence thesis by FUNCT_1:def 2;
    end;
  end;
