Theorems · Theorem · order theory
Order.Ico_pred_left
∀ {α : Type u_1} [inst : LinearOrder α] [inst_1 : PredOrder α] {a b : α},
Order.pred b < a → Set.Ico (Order.pred b) a = insert (Order.pred b) (Set.Ico b a)- Defined in
- Mathlib.Order.SuccPred.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- LinearOrderPredOrder
Around this declaration
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- LinearOrderstatement and proof · cited by 8,572
- Set.Iioproof · cited by 1,166
- Set.Iciproof · cited by 1,070
- Set.Icostatement · cited by 799
- PredOrderstatement and proof · cited by 334
- Order.predstatement and proof · cited by 273
- Set.mem_Iioproof · cited by 49
- Set.inter_insert_of_memproof · cited by 5
- Order.Ici_predproof · cited by 2
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