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pingu
2025-12-30 10:45:04 +01:00
parent ed29a2d98b
commit f22c637eb0
1 changed files with 14 additions and 14 deletions
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@@ -185,20 +185,20 @@ inBoth {A} {Γ} {Γ'} {X} x {X₁} (zero x₁ xs) = zero X Γ'
inBoth {A} {Γ} {Γ'} {X} x {X₁} (succ x₁ xs x₂) = succ X₁ Γ' (x x₂)
weak : Δ / Γ ⊢ A → Γ ⊆ Γ' → Δ / Γ' ⊢ A
weak {Δ} {Γ} {A} {Γ'} (var x) x₁ = var (x₁ x)
weak {Δ} {Γ} {A} {Γ'} (mp x x₂) x₁ = mp (weak x x₁) (weak x₂ x₁)
weak {Δ} {Γ} {A} {Γ'} (∧ᵢ x x₂) x₁ = ∧ᵢ (weak x x₁) (weak x₂ x₁)
weak {Δ} {Γ} {A} {Γ'} (∧ₑ₁ x) x₁ = ∧ₑ₁ (weak x x₁)
weak {Δ} {Γ} {A} {Γ'} (∧ₑ₂ x) x₁ = ∧ₑ₂ (weak x x₁)
weak {Δ} {Γ} {A} {Γ'} (∨ᵢ₁ x) x₁ = ∨ᵢ₁ (weak x x₁)
weak {Δ} {Γ} {A} {Γ'} (∨ᵢ₂ x) x₁ = ∨ᵢ₂ (weak x x₁)
weak {Δ} {Γ} {A} {Γ'} (∨ₑ x x₂ x₃) x₁ = ∨ₑ (weak x x₁) (weak x₂ (inBoth x₁)) (weak x₃ (inBoth x₁))
weak {Δ} {Γ} {A} {Γ'} (⇒ᵢ x) x₁ = ⇒ᵢ (weak x (inBoth x₁))
weak {Δ} {Γ} {A} {Γ'} (¬ᵢ x) x₁ = ¬ᵢ (weak x (inBoth x₁))
weak {Δ} {Γ} {A} {Γ'} (¬ₑ x x₂) x₁ = ¬ₑ (weak x x₁) (weak x₂ x₁)
weak {Δ} {Γ} {A} {Γ'} (⊥ₑ x) x₁ = ⊥ₑ (weak x x₁)
weak {Δ} {Γ} {A} {Γ'} (□ᵢ x) x₁ = □ᵢ x
weak {Δ} {Γ} {A} {Γ'} (□ₑ x x₂) x₁ = □ₑ (weak x x₁) (weak x₂ x₁)
weak (var x) x₁ = var (x₁ x)
weak (mp x x₂) x₁ = mp (weak x x₁) (weak x₂ x₁)
weak (∧ᵢ x x₂) x₁ = ∧ᵢ (weak x x₁) (weak x₂ x₁)
weak (∧ₑ₁ x) x₁ = ∧ₑ₁ (weak x x₁)
weak (∧ₑ₂ x) x₁ = ∧ₑ₂ (weak x x₁)
weak (∨ᵢ₁ x) x₁ = ∨ᵢ₁ (weak x x₁)
weak (∨ᵢ₂ x) x₁ = ∨ᵢ₂ (weak x x₁)
weak (∨ₑ x x₂ x₃) x₁ = ∨ₑ (weak x x₁) (weak x₂ (inBoth x₁)) (weak x₃ (inBoth x₁))
weak (⇒ᵢ x) x₁ = ⇒ᵢ (weak x (inBoth x₁))
weak (¬ᵢ x) x₁ = ¬ᵢ (weak x (inBoth x₁))
weak (¬ₑ x x₂) x₁ = ¬ₑ (weak x x₁) (weak x₂ x₁)
weak (⊥ₑ x) x₁ = ⊥ₑ (weak x x₁)
weak (□ᵢ x) x₁ = □ᵢ x
weak (□ₑ x x₂) x₁ = □ₑ (weak x x₁) (weak x₂ x₁)
weak-modal : Δ / Γ ⊢ A → Δ ⊆ Δ' → Δ' / Γ ⊢ A
weak-modal (var x) x₁ = var x