Theorems · Theorem · combinatorics
Multiset.mem_pi
∀ {α : Type u_1} [inst : DecidableEq α] {β : α → Type u_2} (m : Multiset α) (t : (a : α) → Multiset (β a))
(f : (a : α) → a ∈ m → β a), f ∈ m.pi t ↔ ∀ (a : α) (h : a ∈ m), f a h ∈ t a- Defined in
- Mathlib.Data.Multiset.Pi
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 62 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.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Multisetstatement and proof · cited by 2,627
- Multiset.consproof · cited by 313
- Multiset.induction_onproof · cited by 109
- Multiset.mem_cons_selfproof · cited by 44
- Multiset.mem_cons_of_memproof · cited by 35
- Multiset.mem_consproof · cited by 29
- Multiset.notMem_zeroproof · cited by 17
- Multiset.Pi.consproof · cited by 14
- Multiset.pistatement and proof · cited by 9
- Multiset.pi_consproof · cited by 5
- Multiset.Pi.cons_neproof · cited by 5
- Multiset.Pi.cons_sameproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- Finset.mem_piproof · cited by 5
- List.mem_piproof · cited by 1