Theorems · Theorem · order theory
LE.le.exists_succ_iterate
∀ {α : Type u_1} [inst : Preorder α] [inst_1 : SuccOrder α] [IsSuccArchimedean α] {a b : α},
a ≤ b → ∃ n, Order.succ^[n] a = b- Defined in
- Mathlib.Order.SuccPred.Archimedean
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
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.
- Preorderstatement and proof · cited by 7,952
- Nat.iteratestatement · cited by 740
- Order.succstatement · cited by 633
- SuccOrderstatement and proof · cited by 574
- IsSuccArchimedeanstatement and proof · cited by 88
- IsSuccArchimedean.exists_succ_iterate_of_leproof · cited by 12
Cited by4
Results whose statement or proof uses this declaration.
- Succ.recproof · cited by 10
- Order.IsSuccPrelimit.isMin_of_noMaxproof · cited by 2
- Succ.rec_iffproof · cited by 1
- le_total_of_codirectedproof · cited by 1