reserve A for QC-alphabet;
reserve p, q, r, s for Element of CQC-WFF(A);

theorem
  (( p 'or' q ) '&' ( p 'or' r )) => ( p 'or' ( q '&' r )) in TAUT(A)
proof
  ( 'not' p => q ) => (( 'not' p => r ) => ( 'not' p => ( q '&' r ))) in
  TAUT(A) by Th33;
  then
  ( p 'or' q ) => (( 'not' p => r ) => ( 'not' p => ( q '&' r ))) in TAUT(A)
  by Lm1;
  then ( p 'or' q ) => (( p 'or' r ) => ( 'not' p => ( q '&' r ))) in TAUT(A)
by Lm1;
  then
A1: ( p 'or' q ) => (( p 'or' r ) => ( p 'or' ( q '&' r ))) in TAUT(A) by Lm1;
  (( p 'or' q ) => (( p 'or' r ) => ( p 'or' ( q '&' r )))) => ((( p 'or'
  q ) '&' ( p 'or' r )) => ( p 'or' ( q '&' r ))) in TAUT(A) by Th32;
  hence thesis by A1,CQC_THE1:46;
end;
