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Theorems · Theorem · order theory

Set.restrictPreimage_bijective

∀ {α : Type u_1} {β : Type u_2} (t : Set β) {f : α → β},
  Function.Bijective f → Function.Bijective (t.restrictPreimage f)
Defined in
Mathlib.Data.Set.Restrict
Cited by
2 results in Mathlib
Foundations
Depth 11 from the axioms · uses Classical.choice
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Around this declaration

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

Cardinal.mk_preimage_down · cited by 1Cardinal.mk_preimage_downFunction.Bijective.restrictPreimage · cited by 0Bijective.restrictPreimageSet · cited by 53352SetSet.Elem · cited by 7166Set.ElemSet.preimage · cited by 4946Set.preimageFunction.Bijective · cited by 863Function.BijectiveSet.restrictPreimage · cited by 84Set.restrictPreimageSet.restrictPreimage_surjective · cited by 4Set.restrictPreimage_surj…Set.restrictPreimage_injective · cited by 3Set.restrictPreimage_inje…Set.restrictPreimage_bijectiveCITED BYCITES

Cites7

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Cited by2

Results whose statement or proof uses this declaration.