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Theorems · Theorem · order theory

UpperSet.ext

∀ {α : Type u_1} [inst : LE α] {s t : UpperSet α}, ↑s = ↑t → s = t
Defined in
Mathlib.Order.UpperLower.CompleteLattice
Cited by
29 results in Mathlib
Foundations
Depth 10 from the axioms · uses no axioms
Assumes
LE
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Around this declaration

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

upperClosure_singleton · cited by 8upperClosure_singletonupperClosure_image · cited by 3upperClosure_imageUpperSet.symm_map · cited by 2UpperSet.symm_mapLowerSet.compl_iInf · cited by 1LowerSet.compl_iInfLowerSet.compl_iSup · cited by 1LowerSet.compl_iSupupperClosure_sups · cited by 1upperClosure_supsUpperSet.prod_sup_prod · cited by 1UpperSet.prod_sup_prodLowerSet.compl_bot · cited by 0LowerSet.compl_botUpperSet.map_Ici · cited by 0UpperSet.map_IciUpperSet.map_Ioi · cited by 0UpperSet.map_IoiUpperSet.map_map · cited by 0UpperSet.map_mapUpperSet.map_refl · cited by 0UpperSet.map_reflLowerSet.compl_inf · cited by 0LowerSet.compl_infLowerSet.compl_sInf · cited by 0LowerSet.compl_sInfLowerSet.compl_sSup · cited by 0LowerSet.compl_sSupSet · cited by 53352SetSetLike.coe · cited by 8199SetLike.coeUpperSet · cited by 245UpperSetSetLike.ext' · cited by 60SetLike.ext'UpperSet.extCITED BYCITES

Cites4

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

Cited by29

Results whose statement or proof uses this declaration.