Theorems · Theorem · combinatorics
Finset.sigma_preimage_mk
∀ {α : Type u} {β : α → Type u_1} [inst : DecidableEq α] (s : Finset ((a : α) × β a)) (t : Finset α),
(t.sigma fun a => s.preimage (Sigma.mk a) ⋯) = {a ∈ s | a.fst ∈ t}- Defined in
- Mathlib.Data.Finset.Preimage
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 70 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.
Cites10
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
- SetLike.coestatement · cited by 8,199
- Set.preimagestatement · cited by 4,946
- Finset.filterstatement · cited by 949
- Finset.extproof · cited by 565
- Function.Injective.injOnstatement · cited by 280
- Finset.preimagestatement · cited by 108
- Finset.sigmastatement · cited by 69
- sigma_mk_injectivestatement · cited by 27
- Sigma.etaproof · cited by 25
Cited by3
Results whose statement or proof uses this declaration.
- HasSum.sigmaproof · cited by 8
- Finset.sigma_preimage_mk_of_subsetproof · cited by 1
- HasSum.of_sigmaproof · cited by 1