Theorems · Theorem · logic and foundations
HahnSeries.cardSupp_single_mul_le
∀ {Γ : Type u_1} {R : Type u_2} [inst : PartialOrder Γ] [inst_1 : AddCommMonoid Γ] [inst_2 : IsOrderedCancelAddMonoid Γ]
[inst_3 : NonUnitalNonAssocSemiring R] (x : HahnSeries Γ R) (a : Γ) (r : R),
((HahnSeries.single a) r * x).cardSupp ≤ x.cardSupp- Defined in
- Mathlib.RingTheory.HahnSeries.Cardinal
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- AddCommMonoidstatement and proof · cited by 12,281
- PartialOrderstatement and proof · cited by 6,410
- LE.le.transproof · cited by 3,151
- one_mulproof · cited by 2,841
- Cardinalstatement · cited by 2,598
- NonUnitalNonAssocSemiringstatement and proof · cited by 1,081
- HahnSeriesstatement and proof · cited by 528
- IsOrderedCancelAddMonoidstatement and proof · cited by 359
- ZeroHomstatement · cited by 161
- HahnSeries.singlestatement and proof · cited by 82
- mul_le_mul_leftproof · cited by 31
Cited by1
Results whose statement or proof uses this declaration.
- HahnSeries.cardSupp_inv_leproof · cited by 1