Theorems · Theorem · order theory

Set.uIcc_subset_uIcc_left

∀ {α : Type u_1} [inst : Lattice α] {a b x : α}, x ∈ Set.uIcc a b → Set.uIcc a x ⊆ Set.uIcc a b

Defined in: Mathlib.Order.Interval.Set.UnorderedInterval
Cited by: 1 results in Mathlib
Foundations: Depth 8 from the axioms · uses no axioms
Assumes: Lattice

Mathlib docs Source Loogle LeanSearch

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.

Setstatement · cited by 53,352
Latticestatement and proof · cited by 916
Set.uIccstatement and proof · cited by 393
Set.left_mem_uIccproof · cited by 17
Set.uIcc_subset_uIccproof · cited by 6

Cited by1

Results whose statement or proof uses this declaration.

Set.abs_sub_left_of_mem_uIccproof · cited by 2