Theorems · Theorem · order theory
not_lt_top_iff
∀ {α : Type u} [inst : PartialOrder α] [inst_1 : OrderTop α] {a : α}, ¬a < ⊤ ↔ a = ⊤- Defined in
- Mathlib.Order.BoundedOrder.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PartialOrderOrderTop
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 · cited by 9,680
- PartialOrderstatement and proof · cited by 6,410
- OrderTopstatement and proof · cited by 493
- lt_top_iff_ne_topproof · cited by 95
- Iff.not_leftproof · cited by 49
Cited by4
Results whose statement or proof uses this declaration.
- StrictMono.apply_eq_top_iffproof · cited by 3
- MvPowerSeries.weightedOrder_mulproof · cited by 2
- StrictAnti.apply_eq_top_iffproof · cited by 1
- IsZGroup.commutator_ltproof · cited by 0