Theorems · Theorem · order theory
isLeast_singleton
∀ {α : Type u_1} [inst : Preorder α] {a : α}, IsLeast {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
- Set.mem_singletonproof · cited by 183
- IsLeaststatement · cited by 122
- ge_of_eqproof · cited by 67
- Set.eq_of_mem_singletonproof · cited by 22
Cited by5
Results whose statement or proof uses this declaration.
- isGLB_singletonproof · cited by 7
- csInf_singletonproof · cited by 6
- isAntichain_and_least_iffproof · cited by 2
- IsLeast.insertproof · cited by 2
- isLeast_pairproof · cited by 0