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refactor(library/data/nat/sub): cleanup 'max' theorems

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Leonardo de Moura 2014-11-18 17:56:42 -08:00
parent e77cd59368
commit dbb3b7c72a
1 changed files with 8 additions and 4 deletions
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library/data/nat/sub.lean
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@ -368,13 +368,17 @@ sub_split
definition max (n m : ℕ) : ℕ := n + (m - n) definition max (n m : ℕ) : ℕ := n + (m - n)
definition min (n m : ℕ) : ℕ := m - (m - n) definition min (n m : ℕ) : ℕ := m - (m - n)
theorem max_le {n m : ℕ} (H : n ≤ m) : n + (m - n) = m := add_sub_le H theorem max_le {n m : ℕ} (H : n ≤ m) : max n m = m :=
add_sub_le H
theorem max_ge {n m : ℕ} (H : n ≥ m) : n + (m - n) = n := add_sub_ge H theorem max_ge {n m : ℕ} (H : n ≥ m) : max n m = n :=
add_sub_ge H
theorem left_le_max (n m : ℕ) : n ≤ n + (m - n) := !le_add_sub_left theorem left_le_max (n m : ℕ) : n ≤ max n m :=
!le_add_sub_left
theorem right_le_max (n m : ℕ) : m ≤ max n m := !le_add_sub_right theorem right_le_max (n m : ℕ) : m ≤ max n m :=
!le_add_sub_right
-- ### absolute difference -- ### absolute difference