Theorems · Theorem · commutative algebra
HahnSeries.leadingCoeff_zero
∀ {Γ : Type u_1} {R : Type u_3} [inst : PartialOrder Γ] [inst_1 : Zero R], HahnSeries.leadingCoeff 0 = 0- Defined in
- Mathlib.RingTheory.HahnSeries.Basic
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PartialOrderZero
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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.coeffproof · cited by 235
- WithTop.recTopCoeproof · cited by 107
- HahnSeries.leadingCoeffstatement · cited by 49
- HahnSeries.orderTop_zeroproof · cited by 22
Cited by12
Results whose statement or proof uses this declaration.
- HahnSeries.order_mul_of_ne_zeroproof · cited by 3
- HahnSeries.inv_singleproof · cited by 3
- HahnSeries.leadingCoeff_eqproof · cited by 3
- HahnSeries.leadingCoeff_eq_zeroproof · cited by 3
- HahnSeries.leadingCoeff_negproof · cited by 1
- HahnSeries.ne_zero_of_eq_add_singleproof · cited by 1
- HahnSeries.addOppositeEquiv_leadingCoeffproof · cited by 1
- HahnModule.coeff_smul_order_add_orderproof · cited by 1
- HahnSeries.leadingCoeff_nonneg_iffproof · cited by 0
- HahnSeries.leadingCoeff_absproof · cited by 0
- HahnSeries.leadingCoeff_mulproof · cited by 0