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chore(library/standard/data/nat/order): remove unnecessary 'proofs'

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Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
This commit is contained in:
Leonardo de Moura 2014-08-20 21:51:41 -07:00
parent 38f46b1290
commit ab404beb01
1 changed files with 4 additions and 8 deletions
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12
library/standard/data/nat/order.lean
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@ -436,14 +436,10 @@ resolve_left (le_or_gt m n) H
theorem not_le_imp_gt {n m : ℕ} (H : ¬ n ≤ m) : n > m :=
resolve_right (le_or_gt n m) H
theorem lt_decidable [instance] (n m : ℕ) : decidable (n < m) :=
le_decidable _ _
theorem gt_decidable [instance] (n m : ℕ) : decidable (n > m) :=
le_decidable _ _
theorem ge_decidable [instance] (n m : ℕ) : decidable (n ≥ m) :=
le_decidable _ _
-- The following three theorems are automatically proved using the instance le_decidable
theorem lt_decidable [instance] (n m : ℕ) : decidable (n < m)
theorem gt_decidable [instance] (n m : ℕ) : decidable (n > m)
theorem ge_decidable [instance] (n m : ℕ) : decidable (n ≥ m)
-- Note: interaction with multiplication under "positivity"