Theorems · Theorem · order theory
Set.prod_surjOn_fst_iff
∀ {β₁ : Type u_8} {β₂ : Type u_9} {t₁ : Set β₁} {t₂ : Set β₂}, Set.SurjOn Prod.fst (t₁ ×ˢ t₂) t₁ ↔ t₁ = ∅ ∨ t₂.Nonempty- Defined in
- Mathlib.Data.Set.Function
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites6
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.Nonemptystatement and proof · cited by 2,627
- SProd.sprodstatement and proof · cited by 1,750
- Set.SurjOnstatement and proof · cited by 186
- Set.prod_emptyproof · cited by 24
- Set.empty_prodproof · cited by 14
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