Theorems · Theorem · combinatorics
Finset.card_lt_card
∀ {α : Type u_1} {s t : Finset α}, s ⊂ t → s.card < t.card- Defined in
- Mathlib.Data.Finset.Card
- Cited by
- 23 results in Mathlib
- Foundations
- Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- Finset.cardstatement · cited by 2,327
- Multiset.card_lt_cardproof · cited by 6
- Finset.val_lt_iffproof · cited by 4
Cited by25
Results whose statement or proof uses this declaration.
- Finset.strongInductionproof · cited by 10
- Ideal.height_le_spanRank_toENat_of_mem_minimalPrimesproof · cited by 5
- Cardinal.card_lt_card_of_right_finiteproof · cited by 3
- Finset.strongDownwardInductionproof · cited by 3
- Finset.card_lt_univ_of_notMemproof · cited by 2
- cauchy_davenport_minOrder_addproof · cited by 2
- Polynomial.eraseLead_support_card_ltproof · cited by 2
- Finite.wellFounded_of_trans_of_irreflproof · cited by 2
- Infinite.of_injective_to_setproof · cited by 1
- cauchy_davenport_minOrder_mulproof · cited by 1
- IsLinearSet.isProperSemilinearSetproof · cited by 1
- Nat.totient_ltproof · cited by 1