reserve x,y,c for set;

theorem
  for x,y,c being non pair set for s being State of BorrowCirc(x,y,c)
for a1,a3 being Element of BOOLEAN st a1 = s.x & a3 = s.c holds (Following s).[
  <*x,c*>,and2a] = 'not' a1 '&' a3
proof
  let x,y,c be non pair set;
  reconsider a = y as Vertex of BorrowStr(x,y,c) by Th6;
  let s be State of BorrowCirc(x,y,c);
  s.a is Element of BOOLEAN;
  hence thesis by Lm1;
end;
