Theorems · Theorem · combinatorics
Finset.filter_congr
∀ {α : Type u_1} {p q : α → Prop} [inst : DecidablePred p] [inst_1 : DecidablePred q] {s : Finset α},
(∀ x ∈ s, p x ↔ q x) → Finset.filter p s = Finset.filter q s- Defined in
- Mathlib.Data.Finset.Filter
- Cited by
- 167 results in Mathlib
- Foundations
- Depth 54 from the axioms, rests on 819 definitions · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidablePredDecidablePred
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.filterstatement · cited by 949
- Finset.eq_of_veqproof · cited by 45
- Multiset.filter_congrproof · cited by 11
Cited by167
Results whose statement or proof uses this declaration.
- Nat.mem_divisorsproof · cited by 22
- ZMod.card_units_eq_totientproof · cited by 15
- Nat.mem_properDivisorsproof · cited by 15
- Finset.filter_ne'proof · cited by 8
- Finset.prod_addproof · cited by 7
- MeasureTheory.SimpleFunc.map_setToSimpleFuncproof · cited by 6
- Equiv.Perm.card_fixedPointsproof · cited by 4
- AlgebraicTopology.DoldKan.decomposition_Qproof · cited by 4
- hammingDist_commproof · cited by 4
- Nat.totient_prime_pow_succproof · cited by 4
- Matrix.mul_adjp_apply_eqproof · cited by 4
- AddSubgroup.leftCoset_cover_filter_FiniteIndex_auxproof · cited by 3