Theorems · Theorem · logic and foundations
Set.Finite.eq_of_subset_of_card_le
∀ {α : Type u_1} {s t : Set α}, t.Finite → s ⊆ t → Nat.card ↑t ≤ Nat.card ↑s → s = t- Defined in
- Mathlib.SetTheory.Cardinal.NatCard
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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.Elemstatement and proof · cited by 7,166
- Set.Finitestatement and proof · cited by 1,814
- Nat.cardstatement and proof · cited by 844
- not_le_of_gtproof · cited by 97
- Set.Finite.card_lt_cardproof · cited by 4
- eq_or_ssubset_of_subsetproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- Subgroup.eq_of_le_of_card_geproof · cited by 3
- AddSubgroup.eq_of_le_of_card_geproof · cited by 1
- Set.eq_top_of_card_le_of_finiteproof · cited by 0
- Set.Finite.equiv_image_eq_iff_subsetproof · cited by 0