Theorems · Theorem · order theory
Order.Ideal.iSup_mem_iff
∀ {P : Type u_1} [inst : CompleteLattice P] {I : Order.Ideal P} {α : Sort u_2} [Finite α] {f : α → P},
⨆ i, f i ∈ I ↔ ∀ (i : α), f i ∈ I- Defined in
- Mathlib.Order.Ideal
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CompleteLatticeFinite
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.
- Equiv.symmproof · cited by 3,681
- Finitestatement and proof · cited by 3,029
- iSupstatement and proof · cited by 2,415
- CompleteLatticestatement and proof · cited by 1,048
- iSup_congr_Propproof · cited by 247
- SupSetproof · cited by 154
- Order.Idealstatement and proof · cited by 102
- iSup_posproof · cited by 61
- Set.finite_univproof · cited by 52
- Equiv.forall_congr_leftproof · cited by 41
- Equiv.pliftproof · cited by 23
- Equiv.iSup_compproof · cited by 14
Cited by1
Results whose statement or proof uses this declaration.
- Order.Ideal.iSup_memproof · cited by 0