Theorems · Theorem · order theory
Order.succ_iterate
∀ {α : Type u_1} [inst : Preorder α] [inst_1 : AddMonoidWithOne α] [inst_2 : SuccAddOrder α] (x : α) (n : ℕ),
Order.succ^[n] x = x + ↑n- Defined in
- Mathlib.Algebra.Order.SuccPred
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- add_zeroproof · cited by 2,707
- Nat.cast_oneproof · cited by 2,501
- Nat.cast_zeroproof · cited by 1,870
- add_assocproof · cited by 746
- Nat.iteratestatement and proof · cited by 740
- Order.succstatement and proof · cited by 633
- Nat.cast_addproof · cited by 586
- AddMonoidWithOnestatement and proof · cited by 313
- Order.succ_eq_add_oneproof · cited by 115
- SuccAddOrderstatement and proof · cited by 108
- Function.iterate_succ_apply'proof · cited by 72
Cited by1
Results whose statement or proof uses this declaration.
- Nat.succ_iterateproof · cited by 1