Theorems · Theorem · logic and foundations
HahnSeries.cardSupp_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 y : HahnSeries Γ R), (x * y).cardSupp ≤ x.cardSupp * y.cardSupp- Defined in
- Mathlib.RingTheory.HahnSeries.Cardinal
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 96 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.
- AddCommMonoidstatement and proof · cited by 12,281
- PartialOrderstatement and proof · cited by 6,410
- 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
- Cardinal.mk_le_mk_of_subsetproof · cited by 37
- HahnSeries.cardSuppstatement · cited by 28
- HahnSeries.support_mul_subsetproof · cited by 7
- Cardinal.mk_add_leproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- HahnSeries.cardSupp_pow_leproof · cited by 1
- HahnSeries.cardSupp_single_mul_leproof · cited by 1
- HahnSeries.cardSupp_mul_single_leproof · cited by 0
- HahnSeries.cardSupp_div_leproof · cited by 0