
theorem Th46:
  for x,b being non pair set for s being State of BitCompCirc(x,b)
for a1,a2 being Element of BOOLEAN st a1 = s.x & a2 = s.b holds (Following s).
CompOutput(x,b) = 'not' a1 'xor' a2 & (Following s).x = a1 & (Following s).b =
  a2
proof
  let x,b be non pair set;
  let s be State of BitCompCirc(x,b);
  let a1,a2 be Element of BOOLEAN;
  assume
A1: a1 = s.x & a2 = s.b;
  thus (Following s).CompOutput(x,b) = xor2a.<*s.x,s.b*> by Th45
    .= 'not' a1 'xor' a2 by A1,Def7;
  thus thesis by A1,Th45;
end;
