Theorems · Theorem · logic and foundations
Cardinal.add_eq_max
∀ {a b : Cardinal.{u_1}}, Cardinal.aleph0 ≤ a → a + b = max a bIf α is an infinite type, then the cardinality of α ⊕ β is the maximum
of the cardinalities of α and β.
- Defined in
- Mathlib.SetTheory.Cardinal.Arithmetic
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LE.le.transproof · cited by 3,151
- Cardinalstatement and proof · cited by 2,598
- le_antisymmproof · cited by 2,068
- add_le_addproof · cited by 666
- Cardinal.aleph0statement and proof · cited by 521
- le_max_leftproof · cited by 215
- le_max_rightproof · cited by 205
- max_leproof · cited by 71
- self_le_add_leftproof · cited by 18
- self_le_add_rightproof · cited by 17
- Cardinal.add_eq_selfproof · cited by 4
Cited by13
Results whose statement or proof uses this declaration.
- Cardinal.add_mk_eq_maxproof · cited by 3
- Cardinal.add_eq_leftproof · cited by 3
- Cardinal.ciSup_addproof · cited by 2
- FirstOrder.Language.Term.card_sigmaproof · cited by 1
- FirstOrder.Language.exists_elementaryEmbedding_card_eq_of_geproof · cited by 1
- FirstOrder.Language.exists_elementarySubstructure_card_eqproof · cited by 1
- FirstOrder.Language.BoundedFormula.card_leproof · cited by 1
- Cardinal.add_eq_left_iffproof · cited by 1
- Cardinal.add_eq_max'proof · cited by 1
- Cardinal.mk_bounded_set_leproof · cited by 1
- FirstOrder.Language.card_functions_sum_skolem₁proof · cited by 1
- Cardinal.add_le_maxproof · cited by 1