
theorem Th14:
  'not' <*FALSE*> = <*TRUE*>
proof
  now
    let i be Nat;
    assume
A1: i in Seg 1;
    then
A2: i = 1 by FINSEQ_1:2,TARSKI:def 1;
    len <*FALSE*> = 1 by CARD_1:def 7;
    then
A3: (<*FALSE*>/.i) = <*FALSE*>.1 by A2,FINSEQ_4:15;
    len 'not' <*FALSE*> = 1 by CARD_1:def 7;
    hence ('not' <*FALSE*>).i = ('not' <*FALSE*>)/.i by A2,FINSEQ_4:15
      .= 'not' (<*FALSE*>/.i) by A1,BINARITH:def 1
      .= 'not' FALSE by A3
      .= <*TRUE*>.i by A2;
  end;
  hence thesis by FINSEQ_2:119;
end;
