Theorems · Theorem · order theory
iSup_split_single
∀ {α : Type u_1} {β : Type u_2} [inst : CompleteLattice α] (f : β → α) (i₀ : β),
⨆ i, f i = f i₀ ⊔ ⨆ i, ⨆ (_ : i ≠ i₀), f i- Defined in
- Mathlib.Order.CompleteLattice.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 17 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.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- iSupstatement and proof · cited by 2,415
- CompleteLatticestatement and proof · cited by 1,048
- iSup_iSup_eq_leftproof · cited by 15
- iSup_splitproof · cited by 6
Cited by3
Results whose statement or proof uses this declaration.
- iSupIndep.le_iff_eq_of_iSup_eq_topproof · cited by 3
- biSup_le_eq_supproof · cited by 2
- biSup_ge_eq_supproof · cited by 1