Mathlib Map

Theorems · Theorem · order theory

nonneg_add_self_iff

∀ {α : Type u_1} [inst : AddCommMonoid α] [inst_1 : LinearOrder α] [IsOrderedAddMonoid α] {a : α}, 0 ≤ a + a ↔ 0 ≤ a
Defined in
Mathlib.Algebra.Order.Monoid.Defs
Cited by
2 results in Mathlib
Foundations
Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddCommMonoidLinearOrderIsOrderedAddMonoid
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

neg_le_self_iff · cited by 4neg_le_self_iffadd_self_neg_iff · cited by 0add_self_neg_iffAddCommMonoid · cited by 12281AddCommMonoidLinearOrder · cited by 8572LinearOrderIsOrderedAddMonoid · cited by 1659IsOrderedAddMonoidnot_le · cited by 328not_leadd_nonneg · cited by 104add_nonnegadd_neg' · cited by 1add_neg'nonneg_add_self_iffCITED BYCITES

Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.