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fix(library/data/nat/basic): simplify two lemmas

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Leonardo de Moura 2015-10-07 10:32:20 -07:00
parent 3bb09e9959
commit 5f967f40b2
1 changed files with 2 additions and 2 deletions
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library/data/nat/basic.lean
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@ -126,7 +126,7 @@ nat.induction_on m
theorem add.comm [simp] (n m : ℕ) : n + m = m + n :=
nat.induction_on m
(!add_zero ⬝ !zero_add⁻¹)
(by rewrite [add_zero, zero_add])
(take k IH, calc
n + succ k = succ (n+k) : add_succ
... = succ (k + n) : IH
@ -137,7 +137,7 @@ theorem succ_add_eq_succ_add (n m : ℕ) : succ n + m = n + succ m :=
theorem add.assoc [simp] (n m k : ℕ) : (n + m) + k = n + (m + k) :=
nat.induction_on k
(!add_zero ▸ !add_zero)
(by rewrite +add_zero)
(take l IH,
calc
(n + m) + succ l = succ ((n + m) + l) : add_succ