Package bool-def: Basic boolean definitions

Information

Files

• Package tarball bool-def-1.0.tgz
• Theory file bool-def.thy (included in the package tarball)

Defined Constants

• Data
  • Bool
    • ∀
    • ∧
    • ⇒
    • ∃
    • ∃!
    • ∨
    • ¬
    • cond
    • let
    • F
    • T

Theorems

⊦ F ⇔ ∀p. p

⊦ let = λf x. f x

⊦ (¬) = λp. p ⇒ F

⊦ T ⇔ (λp. p) = λp. p

⊦ (∀) = λP. P = λx. T

⊦ (⇒) = λp q. p ∧ q ⇔ p

⊦ (∧) = λp q. (λf. f p q) = λf. f T T

⊦ (∃) = λP. ∀q. (∀x. P x ⇒ q) ⇒ q

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

⊦ (∃!) = λP. (∃) P ∧ ∀x y. P x ∧ P y ⇒ x = y

⊦ cond = λt t1 t2. select x. ((t ⇔ T) ⇒ x = t1) ∧ ((t ⇔ F) ⇒ x = t2)

Input Type Operators

• →
• bool

Input Constants

• =
• Data
  • Bool
    • select