reserve D for non empty set,
  f for FinSequence of D,
  p, p1, p2, p3, q for Element of D,
  i, j, k, l, n for Nat;

theorem Th17:
  Replace(<*p1, p2, p3*>, 3, q) = <*p1, p2, q*>
proof
  set f = <*p1,p2,p3*>;
A1: 3 -'1 = 2 + 1 -'1 .= 2 by NAT_D:34;
A2: len f = 3 by FINSEQ_1:45;
  then
A3: 1 in dom f by FINSEQ_3:25;
A4: 2 in dom f by A2,FINSEQ_3:25;
  3 <= len f by FINSEQ_1:45;
  then Replace(f,3,q) = (f|(3-'1))^<*q*>^(f/^3) by Def1
    .= (f|2)^<*q*>^(f/^len f) by A1,FINSEQ_1:45
    .= (f|2)^<*q*>^{} by RFINSEQ:27
    .= (f|2)^<*q*> by FINSEQ_1:34
    .= <*f/.1,f/.2*>^<*q*> by A2,FINSEQ_5:81
    .= <*f.1*>^<*f/.2*>^<*q*> by A3,PARTFUN1:def 6
    .= <*f.1*>^<*f.2*>^<*q*> by A4,PARTFUN1:def 6
    .= <*p1*>^<*f.2*>^<*q*>
    .= <*p1*>^<*p2*>^<*q*>;
  hence thesis;
end;
