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Theorems · Theorem · order theory

Set.prod_eq_empty_iff

∀ {α : Type u_1} {β : Type u_2} {s : Set α} {t : Set β}, s ×ˢ t = ∅ ↔ s = ∅ ∨ t = ∅
Defined in
Mathlib.Data.Set.Prod
Cited by
8 results in Mathlib
Foundations
Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

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

Set.prod_subset_prod_iff · cited by 15Set.prod_subset_prod_iffUpperSet.prod_eq_top · cited by 0UpperSet.prod_eq_topSublattice.prod_eq_bot · cited by 0Sublattice.prod_eq_botSet.prod_eq_prod_iff · cited by 0Set.prod_eq_prod_iffSet.prod_subset_prod_iff' · cited by 0Set.prod_subset_prod_iff'measurableSet_prod · cited by 0measurableSet_prodLowerSet.prod_eq_bot · cited by 0LowerSet.prod_eq_botisOpen_prod_iff' · cited by 0isOpen_prod_iff'Set · cited by 53352SetSet.Nonempty · cited by 2627Set.NonemptySProd.sprod · cited by 1750SProd.sprodSet.not_nonempty_iff_eq_empty · cited by 56Set.not_nonempty_iff_eq_e…Set.prod_eq_empty_iffCITED BYCITES

Cites4

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Cited by8

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