theorem Th140:
  variables_in 'not' H = variables_in H
proof
A1: rng 'not' H = rng <*2*> \/ rng H by FINSEQ_1:31
    .= {2} \/ rng H by FINSEQ_1:39;
  thus variables_in 'not' H c= variables_in H
  proof
    let a be object;
    assume
A2: a in variables_in 'not' H;
    then a <> 2 by Th137;
    then not a in {2} by TARSKI:def 1;
    then
A3: a in rng H by A1,A2,XBOOLE_0:def 3;
    not a in {0,1,2,3,4} by A2,XBOOLE_0:def 5;
    hence thesis by A3,XBOOLE_0:def 5;
  end;
  thus thesis by A1,XBOOLE_1:7,33;
end;
