Theorems · Theorem · combinatorics
Finset.card_le_card_of_forall_subsingleton
∀ {α : Type u_2} {β : Type u_3} (r : α → β → Prop) {s : Finset α} {t : Finset β},
(∀ a ∈ s, ∃ b ∈ t, r a b) → (∀ b ∈ t, {a | a ∈ s ∧ r a b}.Subsingleton) → s.card ≤ t.card- Cited by
- 2 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Finsetstatement and proof · cited by 13,712
- Set.ofPredstatement and proof · cited by 6,101
- mul_oneproof · cited by 3,885
- Set.Nonemptyproof · cited by 2,627
- Finset.cardstatement and proof · cited by 2,327
- Set.Subsingletonstatement and proof · cited by 276
- Finset.card_posproof · cited by 53
- Finset.coe_nonemptyproof · cited by 18
- Finset.card_le_oneproof · cited by 10
- Finset.card_mul_le_card_mulproof · cited by 6
- Finset.coe_bipartiteAboveproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- Finset.card_le_card_of_forall_subsingleton'proof · cited by 1
- Fintype.card_le_card_of_leftTotal_uniqueproof · cited by 0