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Theorems · Theorem · order theory

add_self_nonpos_iff

∀ {α : Type u_1} [inst : AddCommMonoid α] [inst_1 : LinearOrder α] [IsOrderedAddMonoid α] {a : α}, a + a ≤ 0 ↔ a ≤ 0
Defined in
Mathlib.Algebra.Order.Monoid.Defs
Cited by
0 results in Mathlib
Foundations
Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddCommMonoidLinearOrderIsOrderedAddMonoid
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AddCommMonoid · cited by 12281AddCommMonoidLinearOrder · cited by 8572LinearOrderIsOrderedAddMonoid · cited by 1659IsOrderedAddMonoidnot_le · cited by 328not_lepos_add_self_iff · cited by 2pos_add_self_iffadd_self_nonpos_iffCITED BYCITES

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