
theorem
  'not' <*TRUE*> = <*FALSE*>
proof
  now
    let i be Nat;
    assume
A1: i in Seg 1;
    then
A2: i = 1 by FINSEQ_1:2,TARSKI:def 1;
    len <*TRUE*> = 1 by CARD_1:def 7;
    then
A3: (<*TRUE*>/.i) = <*TRUE*>.1 by A2,FINSEQ_4:15;
    len 'not' <*TRUE*> = 1 by CARD_1:def 7;
    hence ('not' <*TRUE*>).i = ('not' <*TRUE*>)/.i by A2,FINSEQ_4:15
      .= 'not' (<*TRUE*>/.i) by A1,BINARITH:def 1
      .= 'not' TRUE by A3
      .= <*FALSE*>.i by A2;
  end;
  hence thesis by FINSEQ_2:119;
end;
