Theorems · Theorem · order theory
Set.finite_Icc
∀ {α : Type u_1} [inst : Preorder α] [LocallyFiniteOrder α] (a b : α), (Set.Icc a b).Finite- Defined in
- Mathlib.Order.Interval.Finset.Defs
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PreorderLocallyFiniteOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Preorderstatement and proof · cited by 7,952
- Set.Finitestatement · cited by 1,814
- Set.Iccstatement and proof · cited by 1,702
- LocallyFiniteOrderstatement and proof · cited by 658
- Set.toFiniteproof · cited by 174
Cited by13
Results whose statement or proof uses this declaration.
- Ideal.finite_setOfPred_absNorm_leproof · cited by 4
- NumberField.Embeddings.finite_of_norm_leproof · cited by 4
- BddBelow.wellFoundedOn_ltproof · cited by 3
- BddBelow.finite_of_bddAboveproof · cited by 3
- locallyFinite_Icc_of_tendstoproof · cited by 3
- LaurentSeries.Cauchy.coeff_eventually_equalproof · cited by 1
- Rat.finite_rat_abs_sub_lt_one_div_den_sqproof · cited by 1
- Set.finite_iff_bddAboveproof · cited by 1
- NumberField.hermiteTheorem.finite_of_discr_bdd_of_isComplexproof · cited by 1
- NumberField.hermiteTheorem.finite_of_discr_bdd_of_isRealproof · cited by 1
- BddAbove.finite_of_bddBelowproof · cited by 1
- Set.ordConnected_iff_disjoint_Ioo_emptyproof · cited by 0