Theorems · Theorem · order theory
Finset.Ioc_pred_left_eq_Icc_of_not_isMin
∀ {α : Type u_1} [inst : LinearOrder α] [inst_1 : LocallyFiniteOrder α] [inst_2 : PredOrder α] {a : α},
¬IsMin a → ∀ (b : α), Finset.Ioc (Order.pred a) b = Finset.Icc a b- Defined in
- Mathlib.Order.Interval.Finset.SuccPred
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 59 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.
- Finsetstatement · cited by 13,712
- LinearOrderstatement and proof · cited by 8,572
- LocallyFiniteOrderstatement and proof · cited by 658
- Finset.Iccstatement and proof · cited by 348
- PredOrderstatement and proof · cited by 334
- Finset.Iocstatement and proof · cited by 301
- IsMinstatement and proof · cited by 277
- Order.predstatement and proof · cited by 273
- Finset.coe_injectiveproof · cited by 127
- Finset.coe_Iccproof · cited by 60
- Finset.coe_Iocproof · cited by 55
- Set.Ioc_pred_left_eq_Icc_of_not_isMinproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Finset.Ioc_sub_one_left_eq_Icc_of_not_isMinproof · cited by 0