Theorems · Theorem · order theory
Multiset.le_inf
∀ {α : Type u_1} [inst : SemilatticeInf α] [inst_1 : OrderTop α] {s : Multiset α} {a : α}, a ≤ s.inf ↔ ∀ b ∈ s, a ≤ b- Defined in
- Mathlib.Data.Multiset.Lattice
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Quot.sound
- Assumes
- SemilatticeInfOrderTop
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- SemilatticeInfstatement and proof · cited by 634
- OrderTopstatement and proof · cited by 493
- le_topproof · cited by 411
- Multiset.induction_onproof · cited by 109
- le_inf_iffproof · cited by 48
- IsEmpty.forall_iffproof · cited by 39
- Multiset.mem_consproof · cited by 29
- Multiset.infstatement and proof · cited by 19
- Multiset.notMem_zeroproof · cited by 17
- Multiset.inf_consproof · cited by 5
- Multiset.inf_zeroproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- Finset.le_inf_iffproof · cited by 12
- Multiset.inf_leproof · cited by 1
- Multiset.inf_monoproof · cited by 0