Theorems · Theorem · combinatorics
Multiset.induction_on
∀ {α : Type u_1} {p : Multiset α → Prop} (s : Multiset α), p 0 → (∀ (a : α) (s : Multiset α), p s → p (a ::ₘ s)) → p s- Defined in
- Mathlib.Data.Multiset.ZeroCons
- Cited by
- 109 results in Mathlib
- Foundations
- Depth 14 from the axioms, rests on 30 definitions · uses 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.consstatement and proof · cited by 313
- Multiset.inductionproof · cited by 31
Cited by109
Results whose statement or proof uses this declaration.
- Multiset.fold_addproof · cited by 9
- Equiv.Perm.sign_of_cycleTypeproof · cited by 7
- Multiset.inter_le_rightproof · cited by 6
- Multiset.lcm_dvdproof · cited by 6
- Polynomial.monic_multiset_prod_of_monicproof · cited by 6
- Associates.prod_mkproof · cited by 6
- Directed.finset_leproof · cited by 6
- Multiset.rel_refl_of_refl_onproof · cited by 5
- Multiset.sum_map_mul_rightproof · cited by 5
- DFinsupp.inductionproof · cited by 5
- Multiset.bind_mapproof · cited by 5
- Multiset.bind_singletonproof · cited by 5