Theorems · Definition · order theory
WithTop.pred
{α : Type u_1} → [inst : Preorder α] → [OrderTop α] → [PredOrder α] → WithTop α → αThe predecessor of a : WithTop α as an element of α.
- Defined in
- Mathlib.Order.SuccPred.WithBot
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 6 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.
- Top.topproof · cited by 9,680
- Preorderstatement and proof · cited by 7,952
- WithTopstatement and proof · cited by 3,754
- OrderTopstatement and proof · cited by 493
- PredOrderstatement and proof · cited by 334
- Order.predproof · cited by 273
- WithTop.recTopCoeproof · cited by 107
Cited by8
Results whose statement or proof uses this declaration.
- WithTop.pred_monostatement and proof · cited by 1
- WithTop.pred_strictMonostatement and proof · cited by 1
- WithTop.pred_coestatement · cited by 0
- WithTop.pred_eq_predstatement and proof · cited by 0
- WithTop.pred_eq_topstatement · cited by 0
- WithTop.pred_le_predstatement · cited by 0
- WithTop.pred_lt_predstatement · cited by 0
- WithTop.pred_topstatement · cited by 0