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Theorems · Theorem · order theory

LowerSet.ext

∀ {α : Type u_1} [inst : LE α] {s t : LowerSet 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.

lowerClosure_singleton · cited by 8lowerClosure_singletonlowerClosure_image · cited by 3lowerClosure_imageLowerSet.symm_map · cited by 2LowerSet.symm_maplowerClosure_infs · cited by 1lowerClosure_infsUpperSet.compl_iInf · cited by 1UpperSet.compl_iInfUpperSet.compl_iSup · cited by 1UpperSet.compl_iSupLowerSet.prod_inf_prod · cited by 1LowerSet.prod_inf_prodLowerSet.ext_iff · cited by 1LowerSet.ext_iffLowerSet.map_Iic · cited by 0LowerSet.map_IicLowerSet.map_Iio · cited by 0LowerSet.map_IioLowerSet.map_map · cited by 0LowerSet.map_mapLowerSet.map_refl · cited by 0LowerSet.map_reflLowerSet.compl_compl · cited by 0LowerSet.compl_complLowerSet.Iic_inf · cited by 0LowerSet.Iic_infUpperSet.compl_bot · cited by 0UpperSet.compl_botSet · cited by 53352SetSetLike.coe · cited by 8199SetLike.coeLowerSet · cited by 230LowerSetSetLike.ext' · cited by 60SetLike.ext'LowerSet.extCITED BYCITES

Cites4

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Cited by29

Results whose statement or proof uses this declaration.