Theorems · Theorem · order theory
Order.pred_le_pred
∀ {α : Type u_1} [inst : Preorder α] [inst_1 : PredOrder α] {a b : α}, b ≤ a → Order.pred b ≤ Order.pred a- Defined in
- Mathlib.Order.SuccPred.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- PredOrderstatement and proof · cited by 334
- IsMinproof · cited by 277
- Order.predstatement and proof · cited by 273
- LE.le.trans'proof · cited by 140
- LT.lt.trans_le'proof · cited by 52
- LE.le.lt_of_not_geproof · cited by 21
- Order.pred_leproof · cited by 19
- Order.le_pred_of_ltproof · cited by 15
- Order.le_pred_iff_of_not_isMinproof · cited by 14
- Order.pred_lt_of_le_of_not_isMinproof · cited by 4
- IsMin.monoproof · cited by 3
Cited by5
Results whose statement or proof uses this declaration.
- Order.pred_monoproof · cited by 3
- Order.pred_le_iff_le_succproof · cited by 1
- WithTop.pred_monoproof · cited by 1
- Order.pred_lt_topproof · cited by 1
- Order.le_succ_iff_pred_leproof · cited by 0