Theorems · Theorem · commutative algebra
HahnSeries.coeff_one
∀ {Γ : Type u_1} {R : Type u_3} [inst : Zero Γ] [inst_1 : PartialOrder Γ] [inst_2 : Zero R] [inst_3 : One R] {a : Γ},
HahnSeries.coeff 1 a = if a = 0 then 1 else 0- Cited by
- 14 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- ZeroPartialOrderZeroOne
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- PartialOrderstatement and proof · cited by 6,410
- HahnSeriesstatement · cited by 528
- HahnSeries.coeffstatement · cited by 235
- HahnSeries.coeff_singleproof · cited by 4
Cited by14
Results whose statement or proof uses this declaration.
- HahnSeries.single_powproof · cited by 5
- HahnSeries.SummableFamily.powers_zeroproof · cited by 4
- HahnSeries.SummableFamily.orderTop_hsum_binomialFamily_posproof · cited by 3
- HahnSeries.SummableFamily.powerSeriesFamily_of_not_orderTop_posproof · cited by 2
- HahnSeries.leadingCoeff_oneproof · cited by 1
- HahnSeries.cardSupp_inv_leproof · cited by 1
- HahnSeries.SummableFamily.support_pow_subset_closureproof · cited by 1
- HahnSeries.SummableFamily.support_powerSeriesFamily_subsetproof · cited by 1
- HahnSeries.SummableFamily.powerSeriesFamily_hsum_zeroproof · cited by 1
- HahnSeries.SummableFamily.binomialFamily_mem_supportproof · cited by 1
- PowerSeries.coeff_heval_zeroproof · cited by 0
- HahnSeries.isUnit_iffproof · cited by 0