Theorems · Theorem · order theory
Order.Ici_subset_Ioi_pred_of_not_isMin
Deprecated since 2026-06-06Mathlib marks this declaration as deprecated.
∀ {α : Type u_1} [inst : Preorder α] [inst_1 : PredOrder α] {a : α}, ¬IsMin a → Set.Ici a ⊆ Set.Ioi (Order.pred a)- Defined in
- Mathlib.Order.SuccPred.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses propext
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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.Ioistatement · cited by 1,463
- Set.Icistatement · cited by 1,070
- PredOrderstatement and proof · cited by 334
- IsMinstatement and proof · cited by 277
- Order.predstatement · cited by 273
- Set.Ici_subset_Ioiproof · cited by 15
- Order.pred_lt_of_not_isMinproof · cited by 9
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