Mathlib Map

Theorems · Theorem · order theory

UpperSet.upper

∀ {α : Type u_1} [inst : LE α] (s : UpperSet α), IsUpperSet ↑s
Defined in
Mathlib.Order.UpperLower.CompleteLattice
Cited by
11 results in Mathlib
Foundations
Depth 10 from the axioms · uses no axioms
Assumes
LE
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

le_upperClosure · cited by 3le_upperClosureSet.OrdConnected.null_frontier · cited by 2OrdConnected.null_frontierUpperSet.le_Ici · cited by 1UpperSet.le_IciupperClosure_interior_subset · cited by 0upperClosure_interior_sub…upperClosure_interior_subset' · cited by 0upperClosure_interior_sub…Set.OrdConnected.vadd · cited by 0OrdConnected.vaddclosure_upperClosure_comm_pi · cited by 0closure_upperClosure_comm…ordConnected_iff_upperClosure_inter_lowerClosure · cited by 0ordConnected_iff_upperClo…upperClosure_eq · cited by 0upperClosure_eqSet.OrdConnected.smul · cited by 0OrdConnected.smulSet.OrdConnected.interior · cited by 0OrdConnected.interiorSetLike.coe · cited by 8199SetLike.coeUpperSet · cited by 245UpperSetIsUpperSet · cited by 148IsUpperSetUpperSet.upper' · cited by 2UpperSet.upper'UpperSet.upperCITED BYCITES

Cites4

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

Cited by11

Results whose statement or proof uses this declaration.