Theorems · Theorem · combinatorics
List.mem_pi
∀ {ι : Type u_1} [inst : DecidableEq ι] {α : ι → Type u_2} {l : List ι} (fs : (i : ι) → List (α i))
(f : (i : ι) → i ∈ l → α i), f ∈ l.pi fs ↔ ∀ (i : ι) (hi : i ∈ l), f i hi ∈ fs i- Defined in
- Mathlib.Data.List.Pi
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 63 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.
- Multiset.ofListproof · cited by 290
- List.pistatement · cited by 5
- Multiset.mem_piproof · cited by 2
- Multiset.pi_coeproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- List.mem_pi_toListproof · cited by 1