Theorems · Theorem · order theory
Finite.le_ciSup_of_le
∀ {α : Type u_1} {ι : Type u_2} [Finite ι] [inst : ConditionallyCompleteLattice α] {a : α} {f : ι → α} (c : ι),
a ≤ f c → a ≤ iSup f- Defined in
- Mathlib.Data.Fintype.Order
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Finitestatement and proof · cited by 3,029
- iSupstatement · cited by 2,415
- ConditionallyCompleteLatticestatement and proof · cited by 364
- le_ciSup_of_leproof · cited by 22
- Finite.bddAbove_rangeproof · cited by 11
Cited by17
Results whose statement or proof uses this declaration.
- Finite.le_ciSupproof · cited by 10
- Height.one_le_mulHeightproof · cited by 8
- Finite.map_iSup_of_monotoneOnproof · cited by 3
- Height.mulHeight_sumElim_zero_eqproof · cited by 3
- Rat.mulHeight₁_eq_maxproof · cited by 2
- IsNonarchimedean.apply_sum_leproof · cited by 2
- partialSups_eq_ciSup_Iicproof · cited by 2
- Height.mulHeight_comp_leproof · cited by 2
- IsNonarchimedean.eval_mvPolynomial_leproof · cited by 1
- IsNonarchimedean.iSup_abv_linearMap_apply_leproof · cited by 1
- Rat.iSup_finitePlace_apply_eq_one_of_gcd_eq_oneproof · cited by 1
- Finite.ciSup_supproof · cited by 1