Theorems · Theorem · logic and foundations
Cardinal.bddAbove_of_small
∀ {s : Set Cardinal.{u}} [h : Small.{u, u + 1} ↑s], BddAbove s- Defined in
- Mathlib.SetTheory.Cardinal.Basic
- Cited by
- 37 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Small
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Cited by37
Results whose statement or proof uses this declaration.
- Module.Basis.mk_eq_rank''proof · cited by 23
- Ordinal.bddAbove_of_smallproof · cited by 19
- LinearIndependent.cardinal_lift_le_rankproof · cited by 16
- Cardinal.preBeth_strictMonoproof · cited by 9
- IsLocalizedModule.lift_rank_eqproof · cited by 7
- lift_rank_range_leproof · cited by 7
- Cardinal.preBeth_limitproof · cited by 5
- lift_rank_le_of_injective_injectiveₛproof · cited by 5
- AlgebraicIndependent.lift_cardinalMk_le_trdegproof · cited by 4
- Cardinal.sum_le_lift_mk_mul_iSup_liftproof · cited by 4
- Matroid.IsBase.cardinalMk_le_cRankproof · cited by 3
- exists_finset_linearIndependent_of_le_rankproof · cited by 3