
theorem Th28:
  for A, B being Subset of [:I[01],I[01]:] st A = [:[.0,1/2.], [.0
,1.]:] & B = [:[.1/2,1.], [.0,1.]:] holds [#] ([:I[01],I[01]:] | A) \/ [#] ([:
  I[01],I[01]:] | B) = [#] [:I[01],I[01]:]
proof
  let A, B be Subset of [:I[01],I[01]:];
  assume
A1: A = [:[.0,1/2.], [.0,1.]:] & B = [:[.1/2,1.], [.0,1.]:];
  [#] ([:I[01],I[01]:] | A) \/ [#] ([:I[01],I[01]:] | B) = A \/ [#] ([:
  I[01],I[01]:] | B) by PRE_TOPC:def 5
    .= A \/ B by PRE_TOPC:def 5
    .= [:[.0,1/2.] \/ [.1/2,1.], [.0,1.]:] by A1,ZFMISC_1:97
    .= [:[.0,1.], [.0,1.]:] by XXREAL_1:174
    .= [#] [:I[01],I[01]:] by BORSUK_1:40,def 2;
  hence thesis;
end;
