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[Merged by Bors] - feat(algebra/order/monoid) Add zero_le_three and zero_le_four #15219

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[Merged by Bors] - feat(algebra/order/monoid) Add zero_le_three and zero_le_four #15219

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8 changes: 8 additions & 0 deletions src/algebra/order/monoid.lean
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Expand Up @@ -120,6 +120,14 @@ lemma zero_le_two [preorder α] [has_one α] [add_zero_class α] [zero_le_one_cl
[covariant_class α α (+) (≤)] : (0 : α) ≤ 2 :=
add_nonneg zero_le_one zero_le_one

lemma zero_le_three [preorder α] [has_one α] [add_zero_class α] [zero_le_one_class α]
[covariant_class α α (+) (≤)] : (0 : α) ≤ 3 :=
add_nonneg zero_le_two zero_le_one

lemma zero_le_four [preorder α] [has_one α] [add_zero_class α] [zero_le_one_class α]
[covariant_class α α (+) (≤)] : (0 : α) ≤ 4 :=
add_nonneg zero_le_two zero_le_two

lemma one_le_two [has_le α] [has_one α] [add_zero_class α] [zero_le_one_class α]
[covariant_class α α (+) (≤)] : (1 : α) ≤ 2 :=
calc 1 = 1 + 0 : (add_zero 1).symm
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