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Theorems · Theorem · group theory

Multiset.prod_induction

∀ {M : Type u_3} [inst : CommMonoid M] (p : M → Prop) (s : Multiset M),
  (∀ (a b : M), p a → p b → p (a * b)) → p 1 → (∀ a ∈ s, p a) → p s.prod
Defined in
Mathlib.Algebra.BigOperators.Group.Multiset.Defs
Cited by
3 results in Mathlib
Foundations
Depth 19 from the axioms · uses propext, Quot.sound
Assumes
CommMonoid
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Around this declaration

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Finset.prod_induction · cited by 18Finset.prod_inductionIdeal.absNorm_relNorm · cited by 2Ideal.absNorm_relNormIdeal.sup_multiset_prod_eq_top · cited by 1Ideal.sup_multiset_prod_e…Multiset · cited by 2627MultisetCommMonoid · cited by 2264CommMonoidMultiset.prod · cited by 528Multiset.prodMultiset.foldr_induction · cited by 2Multiset.foldr_inductionMultiset.prod_eq_foldr · cited by 1Multiset.prod_eq_foldrMultiset.prod_inductionCITED BYCITES

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Cited by3

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