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