Package bool-ext: Boolean extensionality theorems

Information

Files

• Package tarball bool-ext-1.1.tgz
• Theory file bool-ext.thy (included in the package tarball)

Theorems

⊦ ∀f g. f = g ⇔ ∀x. f x = g x

⊦ ∀f g. (∀x. f x = g x) ⇒ f = g

Input Type Operators

• →
• bool

Input Constants

• =
• Data
  • Bool
    • ∀
    • ∧
    • ⇒
    • ~
    • F
    • T

Assumptions

⊦ T

⊦ ∀t. (λx. t x) = t

⊦ (∀) = λp. p = λx. T

⊦ (⇒) = λp q. p ∧ q ⇔ p

⊦ (∧) = λp q. (λf. f p q) = λf. f T T

⊦ ∀t. (T ⇒ t ⇔ t) ∧ (t ⇒ T ⇔ T) ∧ (F ⇒ t ⇔ T) ∧ (t ⇒ t ⇔ T) ∧ (t ⇒ F ⇔ ¬t)