Package gfp-div-exp-def: Definition of a GF(p) exponentiation algorithm based on division
Information
| name | gfp-div-exp-def |
| version | 1.5 |
| description | Definition of a GF(p) exponentiation algorithm based on division |
| author | Joe Hurd <joe@gilith.com> |
| license | MIT |
| provenance | HOL Light theory extracted on 2012-03-08 |
| requires | bool list |
| show | Data.Bool Data.List Number.GF(p) |
Files
- Package tarball gfp-div-exp-def-1.5.tgz
- Theory file gfp-div-exp-def.thy (included in the package tarball)
Defined Constant
- Number
- GF(p)
- expDiv
- GF(p)
Theorems
⊦ ∀b n d f p. expDiv b n d f p [] = if b then n / d else d / n
⊦ ∀b n d f p h t.
expDiv b n d f p (h :: t) =
let s ← p / f in expDiv (¬b) d (if h then n / s else n) s f t
Input Type Operators
- →
- bool
- Data
- List
- list
- List
- Number
- GF(p)
- gfp
- GF(p)
Input Constants
- =
- select
- Data
- Bool
- ∀
- ∧
- ⇒
- ∃
- ¬
- cond
- ⊤
- List
- ::
- []
- Bool
- Number
- GF(p)
- /
- GF(p)
Assumptions
⊦ ⊤
⊦ (∃) = λp. p ((select) p)
⊦ (∀) = λp. p = λx. ⊤
⊦ (⇒) = λp q. p ∧ q ⇔ p
⊦ (∧) = λp q. (λf. f p q) = λf. f ⊤ ⊤
⊦ (∃) = λp. ∀q. (∀x. p x ⇒ q) ⇒ q
⊦ ∀p. (∀x. ∃y. p x y) ⇔ ∃y. ∀x. p x (y x)
⊦ ∀NIL' CONS'.
∃fn. fn [] = NIL' ∧ ∀a0 a1. fn (a0 :: a1) = CONS' a0 a1 (fn a1)