18 lines
652 B
Text
18 lines
652 B
Text
instance {α : Type u} {β : Type v} [LE β] : LE (α → β) where
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le f g := ∀ i, f i ≤ g i
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class LE_trans (α : Type u) extends LE α where
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le_trans : ∀ {a b c : α}, a ≤ b → b ≤ c → a ≤ c
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export LE_trans (le_trans)
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instance {α : Type u} {β : Type v} [LE_trans β] : LE_trans (α → β) where
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le_trans h₁ h₂ i := le_trans (h₁ i) (h₂ i)
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example {α β} [LE_trans β] (x y z : α → β) (h₀ : x ≤ y) (h₁ : y ≤ z) : x ≤ z := by
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apply le_trans
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assumption
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assumption
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example {α β} [LE_trans β] (x y z : α → β) (h₀ : x ≤ y) (h₁ : y ≤ z) : x ≤ z := by
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apply le_trans <;> assumption
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