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Theorems · Theorem · order theory

pos_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
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Around this declaration

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

neg_lt_self_iff · cited by 2neg_lt_self_iffadd_self_nonpos_iff · cited by 0add_self_nonpos_iffAddCommMonoid · cited by 12281AddCommMonoidLinearOrder · cited by 8572LinearOrderIsOrderedAddMonoid · cited by 1659IsOrderedAddMonoidnot_lt · cited by 306not_ltadd_pos' · cited by 88add_pos'add_nonpos · cited by 4add_nonpospos_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.