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