Theorems · Theorem · order theory
Order.pred_iterate
∀ {α : Type u_1} [inst : Preorder α] [inst_1 : AddCommGroupWithOne α] [inst_2 : PredSubOrder α] (x : α) (n : ℕ),
Order.pred^[n] x = x - ↑n- Defined in
- Mathlib.Algebra.Order.SuccPred
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 13 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
- Nat.cast_oneproof · cited by 2,501
- Nat.cast_zeroproof · cited by 1,870
- sub_zeroproof · cited by 938
- Nat.iteratestatement and proof · cited by 740
- Nat.cast_addproof · cited by 586
- Order.predstatement and proof · cited by 273
- Function.iterate_succ_apply'proof · cited by 72
- PredSubOrderstatement and proof · cited by 68
- AddCommGroupWithOnestatement and proof · cited by 61
- Order.pred_eq_sub_oneproof · cited by 59
- sub_subproof · cited by 54
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.