Package word16-bits: word16-bits

Information

nameword16-bits
version1.1
descriptionword16-bits
authorJoe Hurd <joe@gilith.com>
licenseMIT
provenanceHOL Light theory extracted on 2011-03-17
showData.Bool

Files

Theorem

w.
    x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15.
      w =
      Data.Word16.Bits.toWord
        (Data.List.:: x0
           (Data.List.:: x1
              (Data.List.:: x2
                 (Data.List.:: x3
                    (Data.List.:: x4
                       (Data.List.:: x5
                          (Data.List.:: x6
                             (Data.List.:: x7
                                (Data.List.:: x8
                                   (Data.List.:: x9
                                      (Data.List.:: x10
                                         (Data.List.:: x11
                                            (Data.List.:: x12
                                               (Data.List.:: x13
                                                  (Data.List.:: x14
                                                     (Data.List.:: x15
                                                        Data.List.[]))))))))))))))))

Input Type Operators

Input Constants

Assumptions

T

n. Number.Natural.≤ Number.Numeral.zero n

F p. p

(¬) = λp. p F

t. (x. t) t

() = λP. P = λx. T

x. x = x T

w. Data.Word16.Bits.toWord (Data.Word16.Bits.fromWord w) = w

w. Data.List.length (Data.Word16.Bits.fromWord w) = Data.Word16.width

n. ¬(Number.Natural.suc n = Number.Numeral.zero)

n. Number.Numeral.bit0 n = Number.Natural.+ n n

Data.Word16.width =
  Number.Numeral.bit0
    (Number.Numeral.bit0
       (Number.Numeral.bit0
          (Number.Numeral.bit0 (Number.Numeral.bit1 Number.Numeral.zero))))

() = λp q. p q p

n. Number.Numeral.bit1 n = Number.Natural.suc (Number.Natural.+ n n)

h t. Data.List.tail (Data.List.:: h t) = t

t h. Data.List.head (Data.List.:: h t) = h

(¬T F) (¬F T)

l. Data.List.length l = Number.Numeral.zero l = Data.List.[]

t1 t2. t1 t2 t2 t1

n.
    Number.Natural.*
      (Number.Numeral.bit0 (Number.Numeral.bit1 Number.Numeral.zero)) n =
    Number.Natural.+ n n

m n. ¬(Number.Natural.< m n Number.Natural.≤ n m)

m n. ¬(Number.Natural.≤ m n Number.Natural.< n m)

m n. Number.Natural.≤ (Number.Natural.suc m) n Number.Natural.< m n

() = λp q. (λf. f p q) = λf. f T T

() = λP. q. (x. P x q) q

m n. Number.Natural.suc m = Number.Natural.suc n m = n

m n.
    Number.Natural.even (Number.Natural.* m n)
    Number.Natural.even m Number.Natural.even n

m n.
    Number.Natural.even (Number.Natural.+ m n) Number.Natural.even m
    Number.Natural.even n

l. l = Data.List.[] h t. l = Data.List.:: h t

() = λp q. r. (p r) (q r) r

(Number.Natural.even Number.Numeral.zero T)
  n. Number.Natural.even (Number.Natural.suc n) ¬Number.Natural.even n

m n. Number.Natural.≤ m n Number.Natural.< m n m = n

m n. Number.Natural.≤ m n Number.Natural.≤ n m m = n

m n.
    Number.Natural.* m n = Number.Numeral.zero
    m = Number.Numeral.zero n = Number.Numeral.zero

Data.List.length Data.List.[] = Number.Numeral.zero
  h t.
    Data.List.length (Data.List.:: h t) =
    Number.Natural.suc (Data.List.length t)

m n p.
    Number.Natural.* m n = Number.Natural.* m p
    m = Number.Numeral.zero n = p

m n p.
    Number.Natural.≤ (Number.Natural.* m n) (Number.Natural.* m p)
    m = Number.Numeral.zero Number.Natural.≤ n p

m n p.
    Number.Natural.< (Number.Natural.* m n) (Number.Natural.* m p)
    ¬(m = Number.Numeral.zero) Number.Natural.< n p

h1 h2 t1 t2. Data.List.:: h1 t1 = Data.List.:: h2 t2 h1 = h2 t1 = t2

(m. Number.Natural.≤ m Number.Numeral.zero m = Number.Numeral.zero)
  m n.
    Number.Natural.≤ m (Number.Natural.suc n)
    m = Number.Natural.suc n Number.Natural.≤ m n

t. ((T t) t) ((t T) t) ((F t) ¬t) ((t F) ¬t)

t. (T t t) (t T t) (F t F) (t F F) (t t t)

t. (T t T) (t T T) (F t t) (t F t) (t t t)

t. (T t t) (t T T) (F t T) (t t T) (t F ¬t)

(n. Number.Natural.+ Number.Numeral.zero n = n)
  (m. Number.Natural.+ m Number.Numeral.zero = m)
  (m n.
     Number.Natural.+ (Number.Natural.suc m) n =
     Number.Natural.suc (Number.Natural.+ m n))
  m n.
    Number.Natural.+ m (Number.Natural.suc n) =
    Number.Natural.suc (Number.Natural.+ m n)