
theorem
  for x,y,z being Element of BOOLEAN holds
   or3a.<*x,y,z*> = nand3b.<*z,y,x*> & or3b.<*x,y,z*> = nand3a.<*z,y,x*>
proof
  let x,y,z be Element of BOOLEAN;
  thus or3a.<*x,y,z*> = 'not' x 'or' y 'or' z by Def15
    .= 'not' ('not' z '&' 'not' y '&' x)
    .= nand3b.<*z,y,x*> by Def14;
  thus or3b.<*x,y,z*> = 'not' x 'or' 'not' y 'or' z by Def16
    .= 'not' ('not' z '&' y '&' x)
    .= nand3a.<*z,y,x*> by Def13;
end;
