Theorems · Theorem · order theory
Finset.sup_sdiff_left
∀ {α : Type u_2} {ι : Type u_5} [inst : BooleanAlgebra α] (s : Finset ι) (f : ι → α) (a : α),
(s.sup fun b => a \ f b) = a \ s.inf f- Defined in
- Mathlib.Data.Finset.Lattice.Fold
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 59 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- BooleanAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- Bot.botproof · cited by 4,720
- Finset.supstatement and proof · cited by 530
- BooleanAlgebrastatement and proof · cited by 300
- Finset.consproof · cited by 221
- Finset.infstatement and proof · cited by 219
- Finset.cons_inductionproof · cited by 85
- Finset.sup_emptyproof · cited by 72
- Finset.sup_consproof · cited by 30
- Finset.inf_consproof · cited by 16
- Finset.inf_emptyproof · cited by 15
- sdiff_infproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- Finset.inf_himp_rightproof · cited by 0