Theorems · Theorem · field theory
Polynomial.cardinalMk_eq_max
∀ {R : Type u} [inst : Semiring R] [Nontrivial R], Cardinal.mk (Polynomial R) = max (Cardinal.mk R) Cardinal.aleph0- Defined in
- Mathlib.Algebra.Polynomial.Cardinal
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringNontrivial
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.
- Semiringstatement and proof · cited by 13,802
- Polynomialstatement · cited by 5,681
- Cardinalstatement · cited by 2,598
- Nontrivialstatement and proof · cited by 2,416
- Cardinal.mkstatement and proof · cited by 942
- Cardinal.liftproof · cited by 583
- Cardinal.aleph0statement and proof · cited by 521
- RingEquiv.toEquivproof · cited by 101
- Cardinal.lift_aleph0proof · cited by 41
- Equiv.cardinal_eqproof · cited by 35
- Cardinal.lift_uzeroproof · cited by 31
- Cardinal.mk_eq_aleph0proof · cited by 20
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.cardinalMk_le_maxproof · cited by 1