Theorems · Theorem · order theory
symmDiff_sup_inf
∀ {α : Type u_2} [inst : GeneralizedCoheytingAlgebra α] (a b : α), symmDiff a b ⊔ a ⊓ b = a ⊔ b- Defined in
- Mathlib.Order.SymmDiff
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses propext
- Assumes
- GeneralizedCoheytingAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- le_antisymmproof · cited by 2,068
- le_sup_rightproof · cited by 242
- symmDiffstatement and proof · cited by 236
- sup_leproof · cited by 159
- le_infproof · cited by 107
- GeneralizedCoheytingAlgebrastatement and proof · cited by 95
- sup_assocproof · cited by 37
- le_sup_of_le_leftproof · cited by 26
- sup_inf_leftproof · cited by 22
- le_sup_of_le_rightproof · cited by 17
- inf_le_supproof · cited by 14
- le_sdiff_supproof · cited by 7
Cited by2
Results whose statement or proof uses this declaration.
- symmDiff_symmDiff_infproof · cited by 1
- inf_sup_symmDiffproof · cited by 0