Theorems · Theorem · order theory
Finite.le_ciSup
∀ {α : Type u_1} {ι : Type u_2} [Finite ι] [inst : ConditionallyCompleteLattice α] (f : ι → α) (i : ι), f i ≤ ⨆ j, f j- Defined in
- Mathlib.Data.Fintype.Order
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 84 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
- le_rflproof · cited by 1,558
- ConditionallyCompleteLatticestatement and proof · cited by 364
- Finite.le_ciSup_of_leproof · cited by 17
Cited by10
Results whose statement or proof uses this declaration.
- Finite.map_iSup_of_monotoneOnproof · cited by 3
- Height.mulHeight_eval_leproof · cited by 3
- spectralNorm_eq_iSup_of_finiteDimensional_normalproof · cited by 2
- Monoid.finite_set_isOfFiniteOrder_of_descentproof · cited by 1
- IsNonarchimedean.eval_mvPolynomial_leproof · cited by 1
- AbsoluteValue.eval_mvPolynomial_leproof · cited by 1
- Finite.ciSup_supproof · cited by 1
- AddMonoid.finite_set_isOfFiniteOrder_of_descentproof · cited by 1
- Matrix.isNilpotent_iff_forall_rowproof · cited by 1
- Finite.ciInf_leproof · cited by 0