Theorems · Theorem · combinatorics
Finset.card_erase_lt_of_mem
∀ {α : Type u_1} {s : Finset α} {a : α} [inst : DecidableEq α], a ∈ s → (s.erase a).card < s.card- Defined in
- Mathlib.Data.Finset.Card
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 54 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEq
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
- Finset.erasestatement · cited by 455
- Multiset.card_erase_lt_of_memproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- Subgroup.exists_finiteIndex_of_leftCoset_cover_auxproof · cited by 2
- AddSubgroup.exists_finiteIndex_of_leftCoset_cover_auxproof · cited by 2
- Dynamics.nonempty_inter_of_coverMincardproof · cited by 0