Theorems · Theorem · order theory
Order.pred_eq_pred_iff_of_not_isMin
∀ {α : Type u_1} [inst : LinearOrder α] [inst_1 : PredOrder α] {a b : α},
¬IsMin a → ¬IsMin b → (Order.pred a = Order.pred b ↔ a = b)- Defined in
- Mathlib.Order.SuccPred.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- LinearOrderPredOrder
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.
- LinearOrderstatement and proof · cited by 8,572
- PredOrderstatement and proof · cited by 334
- IsMinstatement and proof · cited by 277
- Order.predstatement and proof · cited by 273
- eq_iff_ge_not_gtproof · cited by 1
- Order.pred_le_pred_iff_of_not_isMinproof · cited by 1
- Order.pred_lt_pred_iff_of_not_isMinproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- PredOrder.prelimitRecOn_pred_of_not_isMinproof · cited by 2
- Order.isPredPrelimitRecOn_pred_of_not_isMinproof · cited by 2
- Order.pred_eq_pred_iffproof · cited by 1