Theorems · Theorem · commutative algebra
HahnSeries.orderTop_sub_pos
∀ {Γ : Type u_1} {R : Type u_3} [inst : PartialOrder Γ] [inst_1 : Zero Γ] [inst_2 : AddCommGroup R] [inst_3 : One R]
{g : Γ}, 0 < g → ∀ (r : R), 0 < (1 + (HahnSeries.single g) r - 1).orderTop- Cited by
- 1 results in Mathlib
- Foundations
- Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- AddCommGroupstatement and proof · cited by 12,871
- PartialOrderstatement and proof · cited by 6,410
- WithTopstatement · cited by 3,754
- add_zeroproof · cited by 2,707
- map_zeroproof · cited by 1,614
- sub_selfproof · cited by 996
- HahnSeriesstatement · cited by 528
- add_sub_cancel_leftproof · cited by 198
- ZeroHomstatement · cited by 161
- HahnSeries.orderTopstatement and proof · cited by 103
- HahnSeries.singlestatement and proof · cited by 82
Cited by1
Results whose statement or proof uses this declaration.
- HahnSeries.coeff_toOrderTopSubOnePos_powstatement and proof · cited by 0