Theorems · Theorem · order theory
Set.infinite_of_forall_exists_gt
∀ {α : Type u_2} [inst : Preorder α] {s : Set α} [Nonempty α], (∀ (a : α), ∃ b ∈ s, a < b) → s.Infinite- Defined in
- Mathlib.Order.Preorder.Finite
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Preorderstatement and proof · cited by 7,952
- Set.Infinitestatement · cited by 263
- StrictMono.injectiveproof · cited by 94
- strictMono_nat_of_lt_succproof · cited by 21
- Set.infinite_of_injective_forall_memproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Set.infinite_iff_exists_gtproof · cited by 6
- Set.infinite_of_forall_exists_ltproof · cited by 1