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Theorems · Theorem · combinatorics

Multiset.forall_mem_cons

∀ {α : Type u_1} {p : α → Prop} {a : α} {s : Multiset α}, (∀ x ∈ a ::ₘ s, p x) ↔ p a ∧ ∀ x ∈ s, p x
Defined in
Mathlib.Data.Multiset.ZeroCons
Cited by
2 results in Mathlib
Foundations
Depth 15 from the axioms · uses propext, Quot.sound
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Relation.acc_of_singleton · cited by 2Relation.acc_of_singletondivisor_closure_eq_closure · cited by 0divisor_closure_eq_closureMultiset · cited by 2627MultisetMultiset.cons · cited by 313Multiset.consQuotient.inductionOn' · cited by 69Quotient.inductionOn'Multiset.forall_mem_consCITED BYCITES

Cites3

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Cited by2

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