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Theorems · Theorem · order theory

isGLB_singleton

∀ {α : Type u_1} [inst : Preorder α] {a : α}, IsGLB {a} a
Defined in
Mathlib.Order.Bounds.Basic
Cited by
7 results in Mathlib
Foundations
Depth 8 from the axioms · uses no axioms
Assumes
Preorder
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

sInf_singleton · cited by 8sInf_singletonlowerBounds_singleton · cited by 7lowerBounds_singletonisGLB_pair · cited by 5isGLB_pairIsGLB.insert · cited by 3IsGLB.insertbddBelow_singleton · cited by 1bddBelow_singletonIsGLB.mul_left · cited by 1IsGLB.mul_leftCountableInfClosed.singleton · cited by 1CountableInfClosed.single…Set · cited by 53352SetPreorder · cited by 7952PreorderIsGLB · cited by 213IsGLBIsLeast.isGLB · cited by 23IsLeast.isGLBisLeast_singleton · cited by 5isLeast_singletonisGLB_singletonCITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by7

Results whose statement or proof uses this declaration.