Theorems · Theorem · order theory
IsAtom.le_iSup
∀ {ι : Sort u_1} {α : Type u_2} [inst : Order.Frame α] {f : ι → α} {a : α}, IsAtom a → (a ≤ iSup f ↔ ∃ i, a ≤ f i)- Defined in
- Mathlib.Order.Atoms
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Order.Frame
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Bot.botproof · cited by 4,720
- iSupstatement and proof · cited by 2,415
- Disjointproof · cited by 2,201
- le_rflproof · cited by 1,558
- le_transproof · cited by 985
- le_iSupproof · cited by 207
- IsAtomstatement and proof · cited by 130
- le_bot_iffproof · cited by 116
- Order.Framestatement and proof · cited by 88
- of_not_notproof · cited by 51
- le_iff_eq_or_ltproof · cited by 20
- disjoint_iSup_iffproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- IsCoatom.iInf_leproof · cited by 1
- IsAtom.le_sSupproof · cited by 1