Theorems · Theorem · order theory
sdiff_iInf_eq
∀ {α : Type u} {ι : Sort w} [inst : Order.Coframe α] {a : α} {f : ι → α}, a \ ⨅ x, f x = ⨆ x, a \ f x- Defined in
- Mathlib.Order.CompleteBooleanAlgebra
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Quot.sound
- Assumes
- Order.Coframe
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- iSupstatement · cited by 2,415
- iInfstatement · cited by 1,690
- eq_of_forall_ge_iffproof · cited by 96
- iSup_le_iffproof · cited by 45
- Order.Coframestatement and proof · cited by 38
- le_iInf_iffproof · cited by 30
- sdiff_le_iff'proof · cited by 20
- sup_iInf_eqproof · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- sdiff_iSup_eqproof · cited by 0