Theorems · Theorem · order theory
sSup_symmDiff_sSup_le
∀ {α : Type u} [inst : CompleteBooleanAlgebra α] {s t : Set α},
s.Nonempty → t.Nonempty → symmDiff (sSup s) (sSup t) ≤ sSup (Set.image2 (fun x1 x2 => symmDiff x1 x2) s t)- Defined in
- Mathlib.Order.CompleteBooleanAlgebra
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 61 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.
Cites11
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.Nonemptystatement and proof · cited by 2,627
- SupSet.sSupstatement and proof · cited by 954
- Set.image2statement · cited by 311
- symmDiffstatement and proof · cited by 236
- iSup_monoproof · cited by 37
- sSup_imageproof · cited by 36
- CompleteBooleanAlgebrastatement and proof · cited by 32
- sSup_symmDiff_leproof · cited by 3
- sSup_image2proof · cited by 3
- symmDiff_sSup_leproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Set.sUnion_symmDiff_sUnion_subsetproof · cited by 0