Theorems · Theorem · commutative algebra
HahnSeries.orderTop_smul_not_lt
∀ {Γ : Type u_1} {R : Type u_3} [inst : PartialOrder Γ] {V : Type u_8} [inst_1 : Zero V] [inst_2 : SMulZeroClass R V]
(r : R) (x : HahnSeries Γ V), ¬(r • x).orderTop < x.orderTop- Defined in
- Mathlib.RingTheory.HahnSeries.Addition
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 98 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.
- PartialOrderstatement and proof · cited by 6,410
- WithTopstatement and proof · cited by 3,754
- HahnSeriesstatement and proof · cited by 528
- HahnSeries.coeffproof · cited by 235
- SMulZeroClassstatement and proof · cited by 213
- HahnSeries.orderTopstatement and proof · cited by 103
- HahnSeries.orderTop_zeroproof · cited by 22
- not_top_ltproof · cited by 17
- HahnSeries.orderTop_of_ne_zeroproof · cited by 17
- right_ne_zero_of_smulproof · cited by 6
- Function.support_smul_subset_rightproof · cited by 5
- Set.IsWF.min_of_subset_not_lt_minproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- HahnSeries.archimedeanClassMk_le_archimedeanClassMk_iffproof · cited by 1
- HahnSeries.orderTop_le_orderTop_smulproof · cited by 1