
theorem
  for am,bp,cm,dp being non pair set for cin being set st cin <> [<*dp,
GFA2AdderOutput(am,bp,cm)*>,and2] & not cin in InnerVertices BitGFA2Str(am,bp,
cm) for s being State of BitFTA2Circ(am,bp,cm,dp,cin) for a1,a2,a3,a4,a5 being
  Element of BOOLEAN st a1 = s.am & a2 = s.bp & a3 = s.cm & a4 = s.dp & a5 = s.
  cin holds Following(s,4).BitFTA2AdderOutputP(am,bp,cm,dp,cin) = (('not' a1
  'xor' a2 'xor' 'not' a3) '&' 'not' a5) 'or' ('not' a5 '&' a4) 'or' (a4 '&' (
'not' a1 'xor' a2 'xor' 'not' a3)) & Following(s,4).BitFTA2AdderOutputQ(am,bp,
  cm,dp,cin) = 'not' ('not' a1 'xor' a2 'xor' 'not' a3 'xor' a4 'xor' 'not' a5)
  by Lm29,Lm30;
