39 lines
736 B
Text
39 lines
736 B
Text
structure Point where
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x : Nat
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y : Nat
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def f (x : Nat) : Point :=
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let y := x + 1
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{ x, y }
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theorem ex1 : f x = { x, y := x + 1 } :=
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rfl
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def g (p : Point) : Nat :=
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p.x + p.y
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def Set (α : Type u) : Type u :=
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α → Prop
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def Set.empty : Set α :=
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fun a => False
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def Set.insert (s : Set α) (a : α) : Set α :=
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fun x => x = a ∨ s a
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syntax (name := finSet) "{" term,* "}" : term
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macro_rules (kind := finSet)
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| `({ $as,* }) => do
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as.getElems.foldlM (init := ← `(Set.empty)) fun s a => `(Set.insert $s $a)
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#check { 1, 2, 3 }
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#check fun x y => g {x, y}
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#check fun x y : Nat => {x, y}
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#check fun x y : Nat => {x, y : Point}
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theorem ex2 (x y : Nat) : { x, y } = (Set.empty.insert x |>.insert y) :=
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rfl
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