40 lines
822 B
Agda
40 lines
822 B
Agda
module TheHoTTGame.Trinitarianism.AsProps.Quest0Solutions where
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open import TheHoTTGame.Trinitarianism.AsProps.Quest0Preamble
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data ⊤ : Prop where
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trivial : ⊤
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data ⊥ : Prop where
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TrueToTrue : ⊤ → ⊤
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TrueToTrue = λ x → x
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TrueToTrue' : ⊤ → ⊤
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TrueToTrue' x = x
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TrueToTrue'' : ⊤ → ⊤
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TrueToTrue'' trivial = trivial
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TrueToTrue''' : ⊤ → ⊤
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TrueToTrue''' x = trivial
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isZero : ℕ → Prop
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isZero zero = ⊤
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isZero (suc n) = ⊥
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ExistsZero : Σ ℕ isZero
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ExistsZero = zero , trivial
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AllZero→⊥ : ((x : ℕ) → isZero x) → ⊥
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AllZero→⊥ h = h 1
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data _∨_ (P Q : Prop) : Prop where
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left : P → P ∨ Q
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right : Q → P ∨ Q
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DecidableIsZero : (n : ℕ) → (isZero n) ∨ (isZero n → ⊥)
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DecidableIsZero zero = left trivial
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DecidableIsZero (suc n) = right (λ x → x)
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