Theorems · Theorem · logic and foundations
Set.eq_of_subset_of_ncard_le
∀ {α : Type u_1} {s t : Set α},
s ⊆ t → t.ncard ≤ s.ncard → autoParam t.Finite Set.eq_of_subset_of_ncard_le._auto_1 → s = t- Defined in
- Mathlib.Data.Set.Card
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- ENatproof · cited by 4,985
- Set.Finitestatement and proof · cited by 1,814
- Set.ncardstatement and proof · cited by 344
- Set.encardproof · cited by 327
- Set.Finite.subsetproof · cited by 285
- Nat.cast_leproof · cited by 159
- Set.Finite.cast_ncard_eqproof · cited by 28
- Set.Finite.eq_of_subset_of_encard_le'proof · cited by 4
Cited by10
Results whose statement or proof uses this declaration.
- MulAction.IsBlock.eq_univ_of_card_ltproof · cited by 3
- MonoidHom.surjective_of_card_ker_le_divproof · cited by 2
- RootPairing.eq_baseOf_of_linearIndepOn_of_mem_or_neg_mem_closureproof · cited by 2
- MulAction.IsPreprimitive.is_two_motive_of_is_motiveproof · cited by 2
- AddAction.IsBlock.eq_univ_of_card_ltproof · cited by 1
- Set.sep_of_ncard_eqproof · cited by 0
- Set.map_eq_of_subsetproof · cited by 0
- Set.subset_iff_eq_of_ncard_leproof · cited by 0
- Matroid.existsMaximalSubsetProperty_of_bddproof · cited by 0
- AddMonoidHom.surjective_of_card_ker_le_divproof · cited by 0