let n be Element of NAT ; :: thesis: for x, y being FinSequence holds InnerVertices ((n + 1) -BitSubtracterStr (x,y)) = (InnerVertices (n -BitSubtracterStr (x,y))) \/ (InnerVertices (BitSubtracterWithBorrowStr ((x . (n + 1)),(y . (n + 1)),(n -BitBorrowOutput (x,y)))))
let x, y be FinSequence; :: thesis: InnerVertices ((n + 1) -BitSubtracterStr (x,y)) = (InnerVertices (n -BitSubtracterStr (x,y))) \/ (InnerVertices (BitSubtracterWithBorrowStr ((x . (n + 1)),(y . (n + 1)),(n -BitBorrowOutput (x,y)))))
InnerVertices ((n -BitSubtracterStr (x,y)) +* (BitSubtracterWithBorrowStr ((x . (n + 1)),(y . (n + 1)),(n -BitBorrowOutput (x,y))))) = (InnerVertices (n -BitSubtracterStr (x,y))) \/ (InnerVertices (BitSubtracterWithBorrowStr ((x . (n + 1)),(y . (n + 1)),(n -BitBorrowOutput (x,y))))) by FACIRC_1:27;
hence InnerVertices ((n + 1) -BitSubtracterStr (x,y)) = (InnerVertices (n -BitSubtracterStr (x,y))) \/ (InnerVertices (BitSubtracterWithBorrowStr ((x . (n + 1)),(y . (n + 1)),(n -BitBorrowOutput (x,y))))) by Th7; :: thesis: verum