Theorems · Theorem · order theory
iSup_symmDiff_iSup_le
∀ {α : Type u} {ι : Sort w} [inst : CompleteBooleanAlgebra α] {f g : ι → α},
symmDiff (⨆ i, f i) (⨆ i, g i) ≤ ⨆ i, symmDiff (f i) (g i)The symmetric difference of two iSups is at most the iSup of the symmetric differences.
- Defined in
- Mathlib.Order.CompleteBooleanAlgebra
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 57 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- iSupstatement and proof · cited by 2,415
- symmDiffstatement and proof · cited by 236
- sup_commproof · cited by 165
- iSup_monoproof · cited by 37
- CompleteBooleanAlgebrastatement and proof · cited by 32
- symmDiff_commproof · cited by 23
- le_symmDiff_sup_rightproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- iSup_symmDiff_leproof · cited by 3
- biSup_symmDiff_biSup_leproof · cited by 1
- Set.iUnion_symmDiff_iUnion_subsetproof · cited by 0