Package unit-thm: unit-thm

Information

Files

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

Theorems

⊦ ∀f g. f = g

⊦ ∀e. ∃fn. fn Data.Unit.() = e

⊦ ∀e. ∃!fn. fn Data.Unit.() = e

⊦ ∀P. P Data.Unit.() ⇒ ∀x. P x

Input Type Operators

• →
• bool
• Data
  • Unit
    • Data.Unit.unit

Input Constants

• =
• Data
  • Bool
    • ∀
    • ∧
    • ⇒
    • ∃
    • ∃!
    • ¬
    • F
    • T
  • Unit
    • Data.Unit.()

Assumptions

⊦ T

⊦ ∀v. v = Data.Unit.()

⊦ ∀t. (∀x. t) ⇔ t

⊦ (∀) = λP. P = λx. T

⊦ ∀x. x = x ⇔ T

⊦ (⇒) = λp q. p ∧ q ⇔ p

⊦ (∧) = λp q. (λf. f p q) = λf. f T T

⊦ (∃) = λP. ∀q. (∀x. P x ⇒ q) ⇒ q

⊦ ∀f g. f = g ⇔ ∀x. f x = g x

⊦ ∀P. (∃!x. P x) ⇔ (∃x. P x) ∧ ∀x x'. P x ∧ P x' ⇒ x = x'

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

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