15 lines
426 B
Text
15 lines
426 B
Text
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import data.nat
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open nat
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theorem add_assoc (m n k : nat) : m + n + k = m + (n + k) :=
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nat.induction_on k
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(show m + n + 0 = m + (n + 0), from rfl),
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(take k,
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assume IH : m + n + k = m + (n + k),
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show m + n + mysucc k = m + (n + mysucc k), from
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calc
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m + n + mysucc k = mysucc (m + n + k) : rfl
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... = mysucc (m + (n + k)) : IH
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... = m + mysucc (n + k) : rfl
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... = m + (n + mysucc k) : rfl)
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