Theorems · Theorem · order theory
Succ.rec_iff
∀ {α : Type u_1} [inst : Preorder α] [inst_1 : SuccOrder α] [IsSuccArchimedean α] {p : α → Prop},
(∀ (a : α), p a ↔ p (Order.succ a)) → ∀ {a b : α}, a ≤ b → (p a ↔ p b)- Defined in
- Mathlib.Order.SuccPred.Archimedean
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Preorderstatement and proof · cited by 7,952
- Nat.iterateproof · cited by 740
- Order.succstatement and proof · cited by 633
- SuccOrderstatement and proof · cited by 574
- IsSuccArchimedeanstatement and proof · cited by 88
- LE.le.exists_succ_iterateproof · cited by 4
- Function.Iterate.recproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Succ.rec_linearproof · cited by 0