Theorems · Theorem · order theory
WithTop.top_le_iff
∀ {α : Type u_1} [inst : LE α] {x : WithTop α}, ⊤ ≤ x ↔ x = ⊤There is a general version top_le_iff, but this lemma does not require a PartialOrder.
- Defined in
- Mathlib.Order.WithBot
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext, Quot.sound
- Assumes
- LE
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement and proof · cited by 9,680
- WithTopstatement and proof · cited by 3,754
- le_topproof · cited by 411
- WithTop.coe_ne_topproof · cited by 43
- WithTop.not_top_le_coeproof · cited by 4
Cited by13
Results whose statement or proof uses this declaration.
- WithTop.forall_coe_le_iff_leproof · cited by 2
- WithTop.untopD_monoproof · cited by 1
- WithTop.forall_le_coe_iff_leproof · cited by 1
- WithTop.le_ofDual_iffproof · cited by 0
- WithTop.toDual_le_iffproof · cited by 0
- WithTop.toDual_le_toDual_iffproof · cited by 0
- WithTop.map_le_iffproof · cited by 0
- WithTop.le_toDual_iffproof · cited by 0
- WithTop.exists_le_coeproof · cited by 0
- WithTop.forall_le_coeproof · cited by 0
- IsMin.withTopproof · cited by 0
- WithTop.ofDual_le_iffproof · cited by 0