Theorems · Theorem · order theory
Order.Ideal.iSup_mem
∀ {P : Type u_1} [inst : CompleteLattice P] {I : Order.Ideal P} {α : Sort u_2} [Finite α] {f : α → P},
(∀ (i : α), f i ∈ I) → ⨆ i, f i ∈ IAlias of the reverse direction of Order.Ideal.iSup_mem_iff.
- Defined in
- Mathlib.Order.Ideal
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CompleteLatticeFinite
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Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finitestatement and proof · cited by 3,029
- iSupstatement · cited by 2,415
- CompleteLatticestatement and proof · cited by 1,048
- Order.Idealstatement and proof · cited by 102
- Order.Ideal.iSup_mem_iffproof · cited by 1
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