Theorems · Theorem · order theory
Order.Iic_pred_of_not_isMin
∀ {α : Type u_1} [inst : Preorder α] [inst_1 : PredOrder α] {a : α}, ¬IsMin a → Set.Iic (Order.pred a) = Set.Iio a- Defined in
- Mathlib.Order.SuccPred.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Preorderstatement and proof · cited by 7,952
- Set.extproof · cited by 2,266
- Set.Iiostatement · cited by 1,166
- Set.Iicstatement · cited by 1,111
- PredOrderstatement and proof · cited by 334
- IsMinstatement and proof · cited by 277
- Order.predstatement · cited by 273
- Order.le_pred_iff_of_not_isMinproof · cited by 14
Cited by3
Results whose statement or proof uses this declaration.
- Order.Icc_pred_right_of_not_isMinproof · cited by 2
- Order.Ioc_pred_right_of_not_isMinproof · cited by 2
- Order.Iic_predproof · cited by 1