Theorems · Theorem · order theory
subsingleton_of_bot_eq_top
∀ {α : Type u} [inst : PartialOrder α] [inst_1 : BoundedOrder α], ⊥ = ⊤ → Subsingleton α- Defined in
- Mathlib.Order.BoundedOrder.Basic
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
- Assumes
- PartialOrderBoundedOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- PartialOrderstatement and proof · cited by 6,410
- Bot.botstatement and proof · cited by 4,720
- BoundedOrderstatement and proof · cited by 270
- ge_of_eqproof · cited by 67
- subsingleton_of_top_le_botproof · cited by 2
Cited by8
Results whose statement or proof uses this declaration.
- bot_ne_topproof · cited by 24
- subsingleton_iff_bot_eq_topproof · cited by 16
- Ideal.IsNilpotent.induction_onproof · cited by 3
- Set.exists_seq_iSup_eq_top_iff_countableproof · cited by 1
- LieAlgebra.subsingleton_of_hasTrivialRadical_lie_abelianproof · cited by 0
- IntermediateField.subsingleton_of_rank_adjoin_eq_oneproof · cited by 0
- IntermediateField.subsingleton_of_finrank_adjoin_eq_oneproof · cited by 0
- IntermediateField.subsingleton_of_finrank_adjoin_le_oneproof · cited by 0