Theorems · Theorem · logic and foundations
Cardinal.mul_eq_max
∀ {a b : Cardinal.{u_1}}, Cardinal.aleph0 ≤ a → Cardinal.aleph0 ≤ b → a * b = max a bIf α and β are infinite types, then the cardinality of α × β is the maximum
of the cardinalities of α and β.
- Defined in
- Mathlib.SetTheory.Cardinal.Arithmetic
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- mul_oneproof · cited by 3,885
- LE.le.transproof · cited by 3,151
- one_mulproof · cited by 2,841
- Cardinalstatement and proof · cited by 2,598
- le_antisymmproof · cited by 2,068
- Cardinal.aleph0statement and proof · cited by 521
- mul_le_mul'proof · cited by 274
- le_max_leftproof · cited by 215
- le_max_rightproof · cited by 205
- max_leproof · cited by 71
- mul_le_mul_rightproof · cited by 47
- mul_le_mul_leftproof · cited by 31
Cited by8
Results whose statement or proof uses this declaration.
- Cardinal.mul_eq_max_of_aleph0_le_leftproof · cited by 8
- Cardinal.mul_aleph0_eqproof · cited by 6
- Cardinal.aleph0_mul_eqproof · cited by 4
- Cardinal.sum_eq_lift_iSup_of_lift_mk_le_lift_iSupproof · cited by 2
- Cardinal.mul_mk_eq_maxproof · cited by 1
- OreLocalization.cardinalMk_le_maxproof · cited by 1
- AddOreLocalization.cardinalMk_le_maxproof · cited by 1
- Cardinal.aleph_mul_alephproof · cited by 0