Theorems · Theorem · order theory
IsSuccArchimedean.exists_succ_iterate_of_le
∀ {α : Type u_3} {inst : Preorder α} {inst_1 : SuccOrder α} [self : IsSuccArchimedean α] {a b : α},
a ≤ b → ∃ n, Order.succ^[n] a = bIf a ≤ b then one can get to a from b by iterating succ
- Defined in
- Mathlib.Order.SuccPred.Archimedean
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
- Assumes
- IsSuccArchimedean
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
Cited by12
Results whose statement or proof uses this declaration.
- toZ_of_gestatement · cited by 5
- LE.le.exists_succ_iterateproof · cited by 4
- strictMonoOn_of_lt_succproof · cited by 4
- monotoneOn_of_le_succproof · cited by 3
- iterate_succ_toZproof · cited by 2
- toZ_iterate_succ_of_not_isMaxproof · cited by 1
- toZ_nonnegproof · cited by 1
- SuccOrder.forall_ne_bot_iffproof · cited by 1
- toZ_iterate_succ_leproof · cited by 0
- exists_succ_iterate_iff_leproof · cited by 0
- exists_succ_iterate_orproof · cited by 0
- IsSuccArchimedean.of_orderIsoproof · cited by 0