Theorems · Theorem · order theory
IsCoatom.sInf_le
∀ {α : Type u_2} [inst : Order.Coframe α] {s : Set α} {a : α}, IsCoatom a → (sInf s ≤ a ↔ ∃ b ∈ s, b ≤ a)- Defined in
- Mathlib.Order.Atoms
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Order.Coframe
Around this declaration
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Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Set.Elemproof · cited by 7,166
- InfSet.sInfstatement · cited by 935
- IsCoatomstatement and proof · cited by 114
- Order.Coframestatement and proof · cited by 38
- sInf_eq_iInf'proof · cited by 17
- IsCoatom.iInf_leproof · cited by 1
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