Theorems · Theorem · combinatorics
Multiset.forall_mem_map_iff
∀ {α : Type u_1} {β : Type v} {f : α → β} {p : β → Prop} {s : Multiset α},
(∀ y ∈ Multiset.map f s, p y) ↔ ∀ x ∈ s, p (f x)- Defined in
- Mathlib.Data.Multiset.MapFold
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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.mapstatement · cited by 876
- Quotient.inductionOn'proof · cited by 69
Cited by8
Results whose statement or proof uses this declaration.
- Finset.prod_inductionproof · cited by 18
- Finset.sum_inductionproof · cited by 13
- Polynomial.natDegree_multiset_prod_X_sub_C_eq_cardproof · cited by 6
- Finset.le_sum_nonempty_of_subadditive_on_predproof · cited by 3
- Finset.sum_induction_nonemptyproof · cited by 2
- Finset.le_prod_nonempty_of_submultiplicative_on_predproof · cited by 2
- Finset.prod_induction_nonemptyproof · cited by 0
- CanonicallyOrderedAdd.prod_posproof · cited by 0