Theorems · Theorem · order theory

Set.restrictPreimage_surjective

∀ {α : Type u_1} {β : Type u_2} (t : Set β) {f : α → β},
  Function.Surjective f → Function.Surjective (t.restrictPreimage f)

Defined in: Mathlib.Data.Set.Restrict
Cited by: 4 results in Mathlib
Foundations: Depth 10 from the axioms · uses Classical.choice

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Cites4

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

Setstatement and proof · cited by 53,352
Set.Elemstatement and proof · cited by 7,166
Set.preimagestatement · cited by 4,946
Set.restrictPreimagestatement · cited by 84

Cited by4

Results whose statement or proof uses this declaration.

Function.Surjective.restrictPreimageproof · cited by 3
Set.surjective_iff_surjective_of_iUnion_eq_univproof · cited by 2
Set.restrictPreimage_bijectiveproof · cited by 2
exists_nat_bool_continuous_surjective_of_compactproof · cited by 0