Theorems · Theorem · order theory
biSup_symmDiff_biSup_le
∀ {α : Type u} {ι : Sort w} [inst : CompleteBooleanAlgebra α] {p : ι → Prop} {f g : (i : ι) → p i → α},
symmDiff (⨆ i, ⨆ (h : p i), f i h) (⨆ i, ⨆ (h : p i), g i h) ≤ ⨆ i, ⨆ (h : p i), symmDiff (f i h) (g i h)A biSup version of iSup_symmDiff_iSup_le.
- Defined in
- Mathlib.Order.CompleteBooleanAlgebra
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 58 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.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- iSupstatement · cited by 2,415
- le_transproof · cited by 985
- symmDiffstatement · cited by 236
- iSup_monoproof · cited by 37
- CompleteBooleanAlgebrastatement and proof · cited by 32
- iSup_symmDiff_iSup_leproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.MeasureDense.of_generateFrom_isSetAlgebra_finiteproof · cited by 1