
theorem
  for ap,bp,cp,dp being non pair set for cin being set st cin <> [<*dp,
GFA0AdderOutput(ap,bp,cp)*>,and2] & not cin in InnerVertices BitGFA0Str(ap,bp,
cp) for s being State of BitFTA0Circ(ap,bp,cp,dp,cin) for a1,a2,a3,a4,a5 being
  Element of BOOLEAN st a1 = s.ap & a2 = s.bp & a3 = s.cp & a4 = s.dp & a5 = s.
  cin holds Following(s,4).BitFTA0AdderOutputP(ap,bp,cp,dp,cin) = ((a1 'xor' a2
  'xor' a3) '&' a5) 'or' (a5 '&' a4) 'or' (a4 '&' (a1 'xor' a2 'xor' a3)) &
  Following(s,4).BitFTA0AdderOutputQ(ap,bp,cp,dp,cin) = a1 'xor' a2 'xor' a3
  'xor' a4 'xor' a5 by Lm9,Lm10;
