theorem for i be Nat st i in dom f holds (nex f)/.i = 'X' (f/.i)
  proof
    let i be Nat;
    reconsider i1 = i as Element of NAT by ORDINAL1:def 12;
    assume
A1: i in dom f;
    then A2: 1 <= i by FINSEQ_3:25;
A3: i <= len f by A1,FINSEQ_3:25;
    then i <= len nex f by Def5;
    hence (nex f)/.i = (nex f).i1 by A2,FINSEQ_4:15
    .= 'X' (f/.i) by Def5,A2,A3;
  end;
