
theorem TTT1:
  for x be object holds <*x*> is disjoint_valued FinSequence
proof
   let x be object;
   now let i,j be object;
    assume A1: i <> j;
A2: dom <*x*> = {1} by FINSEQ_1:2,def 8;
    per cases;
    suppose i in dom <*x*>; then
     i = 1 by A2,TARSKI:def 1; then
     not j in {1} by A1,TARSKI:def 1; then
     <*x*>.j = {} by A2,FUNCT_1:def 2;
     hence <*x*>.i misses <*x*>.j;
    end;
    suppose not i in dom <*x*>; then
     <*x*>.i = {} by FUNCT_1:def 2;
     hence <*x*>.i misses <*x*>.j;
    end;
   end;
   hence thesis by PROB_2:def 2;
end;
