39 lines
813 B
Text
39 lines
813 B
Text
universes u v
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structure InjectiveFunction (α : Type u) (β : Type v) where
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fn : α → β
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inj : ∀ a b, fn a = fn b → a = b
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def add1 : InjectiveFunction Nat Nat where
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fn a := a + 1
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inj a b h := by injection h; assumption
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instance : CoeFun (InjectiveFunction α β) (fun _ => α → β) where
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coe s := s.fn
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#eval add1 10
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def mapAdd1 (xs : List Nat) : List Nat :=
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xs.map add1
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#eval mapAdd1 [1, 2]
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def foo : InjectiveFunction Bool (Nat → Nat) where
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fn
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| true, a => a + 1
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| false, a => a
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inj a b h := by
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cases a
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cases b; rfl; injection (congrFun h 0)
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cases b; injection (congrFun h 0); rfl
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theorem ex1 (x : Nat) : foo true x = x + 1 :=
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rfl
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theorem ex2 (x : Nat) : foo false x = x :=
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rfl
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#eval foo true 10
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#eval foo false 20
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#eval [1, 2, 3].map (foo true)
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