Package word16-bits: 16-bit word to bit-list conversions

Information

name	word16-bits
version	1.79
description	16-bit word to bit-list conversions
author	Joe Leslie-Hurd <joe@gilith.com>
license	MIT
provenance	HOL Light theory extracted on 2014-11-01
checksum	f11712eb895e0fe29b04cf2da15a2306a99b557a
requires	bool list natural word16-def
show	Data.Bool Data.List Data.Word16 Data.Word16.Bits Number.Natural

Files

Package tarball word16-bits-1.79.tgz
Theory source file word16-bits.thy (included in the package tarball)

Theorem

⊦ ∀w.
    ∃x₀ x₁ x₂ x₃ x₄ x₅ x₆ x₇ x₈ x₉ x₁₀ x₁₁ x₁₂ x₁₃ x₁₄ x₁₅.
      w =
      toWord
        (x₀ :: x₁ :: x₂ :: x₃ :: x₄ :: x₅ :: x₆ :: x₇ :: x₈ :: x₉ :: x₁₀ ::
         x₁₁ :: x₁₂ :: x₁₃ :: x₁₄ :: x₁₅ :: [])

External Type Operators

→
bool
Data
- List
  - list
- Word16
  - word16
Number
- Natural
  - natural

External Constants

=
Data
- Bool
  - ∀
  - ∧
  - ⇒
  - ∃
  - ∨
  - ¬
  - ⊥
  - ⊤
- List
  - ::
  - []
  - head
  - length
  - tail
- Word16
  - width
  - Bits
    - fromWord
    - toWord
Number
- Natural
  - +
  - bit0
  - bit1
  - suc
  - zero

Assumptions

⊦ ⊤

⊦ length [] = 0

⊦ bit0 0 = 0

⊦ ∀t. t ⇒ t

⊦ ⊥ ⇔ ∀p. p

⊦ (¬) = λp. p ⇒ ⊥

⊦ ∀t. (∀x. t) ⇔ t

⊦ (∀) = λp. p = λx. ⊤

⊦ ∀t. ⊤ ∧ t ⇔ t

⊦ ∀t. ⊥ ⇒ t ⇔ ⊤

⊦ ∀w. toWord (fromWord w) = w

⊦ ∀w. length (fromWord w) = width

⊦ ∀n. ¬(suc n = 0)

⊦ ∀n. 0 + n = n

⊦ ∀n. bit1 n = suc (bit0 n)

⊦ width = 16

⊦ (⇒) = λp q. p ∧ q ⇔ p

⊦ ∀h t. head (h :: t) = h

⊦ ∀h t. tail (h :: t) = t

⊦ ∀n. bit0 (suc n) = suc (suc (bit0 n))

⊦ ∀l. length l = 0 ⇔ l = []

⊦ ∀h t. length (h :: t) = suc (length t)

⊦ (∧) = λp q. (λf. f p q) = λf. f ⊤ ⊤

⊦ (∃) = λp. ∀q. (∀x. p x ⇒ q) ⇒ q

⊦ ∀m n. m + suc n = suc (m + n)

⊦ ∀m n. suc m + n = suc (m + n)

⊦ ∀m n. suc m = suc n ⇔ m = n

⊦ ∀l. l = [] ∨ ∃h t. l = h :: t

⊦ (∨) = λp q. ∀r. (p ⇒ r) ⇒ (q ⇒ r) ⇒ r

⊦ ∀p. p 0 ∧ (∀n. p n ⇒ p (suc n)) ⇒ ∀n. p n

⊦ ∀h₁ h₂ t₁ t₂. h₁ :: t₁ = h₂ :: t₂ ⇔ h₁ = h₂ ∧ t₁ = t₂