Theorems · Theorem · logic and foundations
HahnSeries.cardSupp_pow_le
∀ {Γ : Type u_1} {R : Type u_2} [inst : PartialOrder Γ] [inst_1 : AddCommMonoid Γ] [inst_2 : IsOrderedCancelAddMonoid Γ]
[inst_3 : Semiring R] (x : HahnSeries Γ R) (n : ℕ), (x ^ n).cardSupp ≤ x.cardSupp ^ n- Defined in
- Mathlib.RingTheory.HahnSeries.Cardinal
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- 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
- pow_zeroproof · cited by 1,094
- HahnSeriesstatement and proof · cited by 528
- pow_succproof · cited by 374
- IsOrderedCancelAddMonoidstatement and proof · cited by 359
- mul_le_mul_leftproof · cited by 31
- HahnSeries.cardSuppstatement and proof · cited by 28
- HahnSeries.cardSupp_mul_leproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- HahnSeries.cardSupp_hsum_powers_leproof · cited by 1