Theorems · Theorem · combinatorics
Multiset.induction
∀ {α : Type u_1} {p : Multiset α → Prop},
p 0 → (∀ (a : α) (s : Multiset α), p s → p (a ::ₘ s)) → ∀ (s : Multiset α), p s- Defined in
- Mathlib.Data.Multiset.ZeroCons
- Cited by
- 31 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
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.consstatement and proof · cited by 313
Cited by31
Results whose statement or proof uses this declaration.
- Multiset.induction_onproof · cited by 109
- Finset.cons_inductionproof · cited by 85
- Multiset.powersetCard_mapproof · cited by 3
- Relation.acc_of_singletonproof · cited by 2
- Multiset.le_prod_of_submultiplicative_on_pred_of_nonnegproof · cited by 2
- Multiset.foldr_induction'proof · cited by 2
- Multiset.map_swap_productproof · cited by 2
- Multiset.filter_joinproof · cited by 1
- Multiset.sum_nat_modproof · cited by 1
- IsUnit.multisetProd_iffproof · cited by 1
- Multiset.prod_int_modproof · cited by 1
- Multiset.prod_joinproof · cited by 1