Theorems · Theorem · order theory
Finset.inf_singleton
∀ {α : Type u_2} {β : Type u_3} [inst : SemilatticeInf α] [inst_1 : OrderTop α] {f : β → α} {b : β}, {b}.inf f = f b- Defined in
- Mathlib.Data.Finset.Lattice.Fold
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Quot.sound
- Assumes
- SemilatticeInfOrderTop
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement · cited by 13,712
- SemilatticeInfstatement and proof · cited by 634
- OrderTopstatement and proof · cited by 493
- Finset.infstatement · cited by 219
- Multiset.inf_singletonproof · cited by 1
Cited by6
Results whose statement or proof uses this declaration.
- MeasureTheory.hahn_decompositionproof · cited by 2
- Submodule.isPrimary_finsetInfproof · cited by 2
- Finset.inf_sdiff_leftproof · cited by 1
- Finset.inf_sdiff_rightproof · cited by 1
- Finset.inf_oneproof · cited by 0
- Finset.inf_zeroproof · cited by 0