Theorems · Theorem · order theory
iInf_split
∀ {α : Type u_1} {β : Type u_2} [inst : CompleteLattice α] (f : β → α) (p : β → Prop),
⨅ i, f i = (⨅ i, ⨅ (_ : p i), f i) ⊓ ⨅ i, ⨅ (_ : ¬p i), f i- Defined in
- Mathlib.Order.CompleteLattice.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CompleteLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Set.ofPredproof · cited by 6,101
- iInfstatement and proof · cited by 1,690
- CompleteLatticestatement and proof · cited by 1,048
- iInf_congr_Propproof · cited by 218
- Set.mem_unionproof · cited by 47
- iInf_posproof · cited by 31
- iInf_unionproof · cited by 5
Cited by4
Results whose statement or proof uses this declaration.
- iInf_split_singleproof · cited by 2
- CompleteLatticeHom.apply_limsup_iterateproof · cited by 2
- nhdsWithin_pi_eqproof · cited by 1
- iInf_extend_topproof · cited by 0