Package group-mult-sub-def: Definition of group multiplication by repeated subtraction
Information
| name | group-mult-sub-def |
| version | 1.12 |
| description | Definition of group multiplication by repeated subtraction |
| author | Joe Leslie-Hurd <joe@gilith.com> |
| license | MIT |
| provenance | HOL Light theory extracted on 2012-12-02 |
| requires | bool group-def group-witness list |
| show | Algebra.Group Data.Bool Data.List |
Files
- Package tarball group-mult-sub-def-1.12.tgz
- Theory source file group-mult-sub-def.thy (included in the package tarball)
Defined Constant
- Algebra
- Group
- multSub
- Group
Theorems
⊦ ∀b n d f p. multSub b n d f p [] = if b then n - d else d - n
⊦ ∀b n d f p h t.
multSub b n d f p (h :: t) =
let s ← p - f in multSub (¬b) d (if h then n - s else n) s f t
External Type Operators
- →
- bool
- Algebra
- Group
- group
- Group
- Data
- List
- list
- List
External Constants
- =
- select
- Algebra
- Group
- -
- Group
- Data
- Bool
- ∀
- ∧
- ⇒
- ∃
- ¬
- cond
- ⊤
- List
- ::
- []
- Bool
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)
⊦ ∀b f. ∃fn. fn [] = b ∧ ∀h t. fn (h :: t) = f h t (fn t)