reserve Y for non empty set;
reserve Y for non empty set;
reserve Y for non empty set;
reserve Y for non empty set,
  a,b,c,d,e,f,g for Function of Y,BOOLEAN;

theorem
  a '&' b '<' c implies a '&' 'not' c '<' 'not' b
proof
  assume a '&' b '<' c;
  then I_el Y = a '&' b 'imp' c by BVFUNC_1:16
    .= 'not' (a '&' b) 'or' c by BVFUNC_4:8
    .= 'not' a 'or' 'not' b 'or' c by BVFUNC_1:14
    .= 'not' a 'or' 'not' 'not' c 'or' 'not' b by BVFUNC_1:8
    .= 'not' (a '&' 'not' c) 'or' 'not' b by BVFUNC_1:14
    .= a '&' 'not' c 'imp' 'not' b by BVFUNC_4:8;
  hence thesis by BVFUNC_1:16;
end;
