Theorems · Theorem · logic and foundations
HahnSeries.cardSupp_mul_single_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),
(x * (HahnSeries.single a) r).cardSupp ≤ x.cardSupp- Defined in
- Mathlib.RingTheory.HahnSeries.Cardinal
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
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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
- mul_oneproof · cited by 3,885
- LE.le.transproof · cited by 3,151
- 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_rightproof · cited by 47
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