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Theorems · Theorem · order theory

nonneg_of_le_add_right

∀ {α : Type u_1} [inst : AddZeroClass α] [inst_1 : LE α] [AddLeftReflectLE α] {a b : α}, a ≤ a + b → 0 ≤ b
Defined in
Mathlib.Algebra.Order.Monoid.Unbundled.Basic
Cited by
2 results in Mathlib
Foundations
Depth 6 from the axioms · uses no axioms
Assumes
AddZeroClassLEAddLeftReflectLE
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Odd.strictMono_pow · cited by 7Odd.strictMono_powexists_nonneg_add_of_le · cited by 5exists_nonneg_add_of_leadd_zero · cited by 2707add_zeroAddZeroClass · cited by 1237AddZeroClassAddLeftReflectLE · cited by 119AddLeftReflectLEle_of_add_le_add_left · cited by 15le_of_add_le_add_leftnonneg_of_le_add_rightCITED BYCITES

Cites4

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Cited by2

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