262 lines
12 KiB
Text
262 lines
12 KiB
Text
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"```lean\nTrue.intro : True\n```\n***\nIntroduction rule for `True`. ",
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"```lean\nTrue.intro : True\n```\n***\nIntroduction rule for `True`. ",
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"```lean\nTrue.intro : True\n```\n***\nIntroduction rule for `True`. ",
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"contents": {"value": "My way better tactic ", "kind": "markdown"}}
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{"value": "```lean\n1 : Nat\n```\n***\nMy notation ", "kind": "markdown"}}
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{"value": "```lean\nNat\n```\n***\nMy way better notation ",
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"contents":
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{"value": "```lean\nNat\n```\n***\nMy ultimate notation ", "kind": "markdown"}}
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"contents": {"value": "My command ", "kind": "markdown"}}
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"contents": {"value": "My way better command ", "kind": "markdown"}}
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"```lean\nid.{0} : ∀ {α : Prop}, α → α\n```\n***\nIdentity function ",
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"contents": {"value": "```lean\nn : Id Nat\n```", "kind": "markdown"}}
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"contents": {"value": "```lean\nfoo : Nat\n```", "kind": "markdown"}}
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"contents": {"value": "```lean\nBar.foo : Nat\n```", "kind": "markdown"}}
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"contents": {"value": "```lean\n_root_.foo : Nat\n```", "kind": "markdown"}}
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"contents": {"value": "```lean\nBar.bar : Nat\n```", "kind": "markdown"}}
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"contents": {"value": "```lean\nBar.Foo : Type\n```", "kind": "markdown"}}
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{"value": "```lean\nBar.Foo.mk : Nat → Foo\n```", "kind": "markdown"}}
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"contents":
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{"value": "```lean\nBar.Foo.hi : Foo → Nat\n```", "kind": "markdown"}}
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"contents": {"value": "```lean\nBar.Bar : Type\n```", "kind": "markdown"}}
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"contents": {"value": "```lean\nBar.Bar.mk : Bar\n```", "kind": "markdown"}}
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{"value": "```lean\nBar.instToStringNat : ToString Nat\n```",
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{"value": "```lean\nBar.f : ToString Nat\n```", "kind": "markdown"}}
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{"value": "A type universe. `Type ≡ Type 0`, `Type u ≡ Sort (u + 1)`. ",
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"contents": {"value": "```lean\nx : Nat\n```", "kind": "markdown"}}
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"`· tac` focuses on the main goal and tries to solve it using `tac`, or else fails. ",
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"```lean\nId Nat\n```\n***\nYou can use parentheses for\n- Grouping expressions, e.g., `a * (b + c)`.\n- Creating tuples, e.g., `(a, b, c)` is notation for `Prod.mk a (Prod.mk b c)`.\n- Performing type ascription, e.g., `(0 : Int)` instructs Lean to process `0` as a value of type `Int`.\n- Creating `Unit.unit`, `()` is just a shorthand for `Unit.unit`.\n- Creating simple functions when combined with `·`. Here are some examples:\n - `(· + 1)` is shorthand for `fun x => x + 1`\n - `(· + ·)` is shorthand for `fun x y => x + y`\n - `(f · a b)` is shorthand for `fun x => f x a b`\n - `(h (· + 1) ·)` is shorthand for `fun x => h (fun y => y + 1) x`\n",
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