reserve a,x,y for object, A,B for set,
  l,m,n for Nat;
reserve X,Y for set, x for object,
  p,q for Function-yielding FinSequence,
  f,g,h for Function;
reserve m,n,k for Nat, R for Relation;
reserve i,j for Nat;
reserve F for Function,
  e,x,y,z for object;
reserve a,b,c for set;

theorem Th123:
  for n st n > 1 holds ((a,b) followed_by c).n = c
proof
  let n;
  assume
A1: n > 1;
  dom (0,1) --> (a,b) = {0,1} by FUNCT_4:62;
  then
A2: not n in dom (0,1) --> (a,b) by A1,TARSKI:def 2;
A3: n in NAT by ORDINAL1:def 12;
  thus ((a,b) followed_by c).n = ((NAT --> c) +* ((0,1) --> (a,b))).n
    .= (NAT --> c).n by A2,FUNCT_4:11
    .= c by A3,FUNCOP_1:7;
end;
