Theorems · Theorem · order theory
IsAtom.Iic_eq
∀ {α : Type u_2} [inst : PartialOrder α] [inst_1 : OrderBot α] {a : α}, IsAtom a → Set.Iic a = {⊥, a}- Defined in
- Mathlib.Order.Atoms
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PartialOrderOrderBot
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- PartialOrderstatement and proof · cited by 6,410
- Bot.botstatement · cited by 4,720
- Set.extproof · cited by 2,266
- Set.Iicstatement · cited by 1,111
- OrderBotstatement and proof · cited by 1,055
- IsAtomstatement and proof · cited by 130
- IsAtom.le_iffproof · cited by 10
Cited by2
Results whose statement or proof uses this declaration.
- Filter.Iic_pureproof · cited by 1
- IsCoatom.Ici_eqproof · cited by 0