Theorems · Theorem · order theory
Set.prod_eq_prod_iff
∀ {α : Type u_1} {β : Type u_2} {s s₁ : Set α} {t t₁ : Set β},
s ×ˢ t = s₁ ×ˢ t₁ ↔ s = s₁ ∧ t = t₁ ∨ (s = ∅ ∨ t = ∅) ∧ (s₁ = ∅ ∨ t₁ = ∅)- Defined in
- Mathlib.Data.Set.Prod
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 59 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites7
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.Nonemptyproof · cited by 2,627
- SProd.sprodstatement and proof · cited by 1,750
- Set.eq_empty_or_nonemptyproof · cited by 248
- Set.nonempty_iff_ne_emptyproof · cited by 96
- Set.prod_eq_empty_iffproof · cited by 8
- Set.prod_eq_prod_iff_of_nonemptyproof · cited by 2
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