Mathlib Map

Theorems · Theorem · order theory

symmDiff_sSup_le

∀ {α : Type u} [inst : CompleteBooleanAlgebra α] {s : Set α},
  s.Nonempty → ∀ {a : α}, symmDiff a (sSup s) ≤ sSup ((fun x => symmDiff a x) '' s)
Defined in
Mathlib.Order.CompleteBooleanAlgebra
Cited by
2 results in Mathlib
Foundations
Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CompleteBooleanAlgebra
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

sSup_symmDiff_sSup_le · cited by 1sSup_symmDiff_sSup_leSet.symmDiff_sUnion_subset · cited by 0Set.symmDiff_sUnion_subsetSet · cited by 53352SetSet.image · cited by 5609Set.imageSet.Nonempty · cited by 2627Set.NonemptySupSet.sSup · cited by 954SupSet.sSupSet.image_congr · cited by 533Set.image_congrsymmDiff · cited by 236symmDiffCompleteBooleanAlgebra · cited by 32CompleteBooleanAlgebrasymmDiff_comm · cited by 23symmDiff_commsSup_symmDiff_le · cited by 3sSup_symmDiff_lesymmDiff_sSup_leCITED BYCITES

Cites9

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Cited by2

Results whose statement or proof uses this declaration.