Theorems · Theorem · order theory
sSup_symmDiff_le
∀ {α : Type u} [inst : CompleteBooleanAlgebra α] {s : Set α},
s.Nonempty → ∀ {a : α}, symmDiff (sSup s) a ≤ sSup ((fun x => symmDiff x a) '' s)- Defined in
- Mathlib.Order.CompleteBooleanAlgebra
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 59 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CompleteBooleanAlgebra
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.
- Setstatement and proof · cited by 53,352
- Set.Elemproof · cited by 7,166
- Set.imagestatement · cited by 5,609
- Set.Nonemptystatement and proof · cited by 2,627
- iSupproof · cited by 2,415
- SupSet.sSupstatement and proof · cited by 954
- symmDiffstatement and proof · cited by 236
- sSup_eq_iSup'proof · cited by 38
- CompleteBooleanAlgebrastatement and proof · cited by 32
- Set.nonempty_coe_sortproof · cited by 23
- sSup_image'proof · cited by 10
- iSup_symmDiff_leproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- symmDiff_sSup_leproof · cited by 2
- sSup_symmDiff_sSup_leproof · cited by 1
- Set.sUnion_symmDiff_subsetproof · cited by 0