34d8ecc066
Recall that `show .. from ..` ensures that proof has exactly the type provided by the user. In the new test, `rw [ih]` without this change because the goal would be ``` ... |- 0 + succ n = succ n ```
15 lines
328 B
Text
15 lines
328 B
Text
namespace Hidden
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open Nat
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theorem zero_add (n : Nat) : 0 + n = n :=
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Nat.recOn (motive := fun x => 0 + x = x)
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n
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(show 0 + 0 = 0 from rfl)
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(fun (n : Nat) (ih : 0 + n = n) =>
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show 0 + succ n = succ n from
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calc
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0 + succ n = succ (0 + n) := rfl
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_ = succ n := by rw [ih])
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end Hidden
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