Mathlib Map

Theorems · Theorem · combinatorics

Finset.card_filter_eq_iff

∀ {α : Type u_1} {s : Finset α} {p : α → Prop} [inst : DecidablePred p],
  (Finset.filter p s).card = s.card ↔ ∀ x ∈ s, p x
Defined in
Mathlib.Data.Finset.Card
Cited by
2 results in Mathlib
Foundations
Depth 58 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
DecidablePred
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Nat.count_iff_forall · cited by 1Nat.count_iff_forallFinset.filter_card_eq · cited by 1Finset.filter_card_eqFinset · cited by 13712FinsetFinset.card · cited by 2327Finset.cardFinset.filter · cited by 949Finset.filterFinset.filter_subset · cited by 55Finset.filter_subsetFinset.card_filter_le · cited by 16Finset.card_filter_leLE.le.ge_iff_eq · cited by 12le.ge_iff_eqFinset.filter_eq_self · cited by 5Finset.filter_eq_selfFinset.eq_iff_card_le_of_subset · cited by 2Finset.eq_iff_card_le_of_…Finset.card_filter_eq_iffCITED BYCITES

Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.