reserve n,i,j,k for Nat;

theorem Th3:
  for f be Function,x,y,z,u,v be object st v <> y holds (f +* ([x,y]
  .--> z)).[u,v]=f.[u,v]
proof
  let f be Function,x,y,z,u,v be object;
  set p=[x,y] .--> z;
  assume v <> y;
  then
A1: [u,v]<>[x,y] by XTUPLE_0:1;
  not [u,v] in dom p by A1,TARSKI:def 1;
  hence thesis by FUNCT_4:11;
end;
