Theorems · Theorem · order theory
isGreatest_singleton
∀ {α : Type u_1} [inst : Preorder α] {a : α}, IsGreatest {a} a- Defined in
- Mathlib.Order.Bounds.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
- Assumes
- Preorder
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.
- Setstatement · cited by 53,352
- Preorderstatement and proof · cited by 7,952
- le_of_eqproof · cited by 366
- Set.mem_singletonproof · cited by 183
- IsGreateststatement · cited by 112
- Set.eq_of_mem_singletonproof · cited by 22
Cited by5
Results whose statement or proof uses this declaration.
- isLUB_singletonproof · cited by 10
- csSup_singletonproof · cited by 6
- isAntichain_and_greatest_iffproof · cited by 2
- IsGreatest.insertproof · cited by 2
- isGreatest_pairproof · cited by 0