Theorems · Theorem · order theory
IsAtomic.exists_atom
∀ (α : Type u_2) [inst : PartialOrder α] [inst_1 : OrderBot α] [Nontrivial α] [IsAtomic α], ∃ a, IsAtom a
- Defined in
- Mathlib.Order.Atoms
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- PartialOrderstatement and proof · cited by 6,410
- Bot.botproof · cited by 4,720
- Nontrivialstatement and proof · cited by 2,416
- OrderBotstatement and proof · cited by 1,055
- IsAtomstatement and proof · cited by 130
- exists_neproof · cited by 101
- IsAtomicstatement and proof · cited by 20
- IsAtomic.eq_bot_or_exists_atom_leproof · cited by 12
Cited by4
Results whose statement or proof uses this declaration.
- IsIsotypic.linearEquiv_funproof · cited by 3
- IsSimpleRing.tfaeproof · cited by 1
- IsIsotypic.linearEquiv_finsuppproof · cited by 0
- IsSemisimpleModule.exists_simple_submoduleproof · cited by 0