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Theorems · Theorem · order theory

symmDiff_iSup_le

∀ {α : Type u} {ι : Sort w} [inst : CompleteBooleanAlgebra α] {f : ι → α} [Nonempty ι] {a : α},
  symmDiff a (⨆ i, f i) ≤ ⨆ i, symmDiff a (f i)
Defined in
Mathlib.Order.CompleteBooleanAlgebra
Cited by
1 results in Mathlib
Foundations
Depth 59 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CompleteBooleanAlgebraNonempty
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Set.symmDiff_iUnion_subset · cited by 0Set.symmDiff_iUnion_subsetiSup · cited by 2415iSupsymmDiff · cited by 236symmDiffCompleteBooleanAlgebra · cited by 32CompleteBooleanAlgebrasymmDiff_comm · cited by 23symmDiff_commiSup_symmDiff_le · cited by 3iSup_symmDiff_lesymmDiff_iSup_leCITED BYCITES

Cites5

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Cited by1

Results whose statement or proof uses this declaration.