Theorems · Theorem · commutative algebra
HahnSeries.min_orderTop_le_orderTop_add
∀ {R : Type u_3} [inst : AddMonoid R] {Γ : Type u_8} [inst_1 : LinearOrder Γ] {x y : HahnSeries Γ R},
min x.orderTop y.orderTop ≤ (x + y).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
- Assumes
- AddMonoidLinearOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LinearOrderstatement and proof · cited by 8,572
- WithTopstatement and proof · cited by 3,754
- AddMonoidstatement and proof · cited by 2,864
- add_zeroproof · cited by 2,707
- zero_addproof · cited by 2,366
- WithTop.someproof · cited by 1,128
- HahnSeriesstatement and proof · cited by 528
- inf_of_le_leftproof · cited by 186
- inf_of_le_rightproof · cited by 128
- HahnSeries.orderTopstatement and proof · cited by 103
- WithTop.coe_le_coeproof · cited by 65
- Set.IsWF.minproof · cited by 47
Cited by2
Results whose statement or proof uses this declaration.
- HahnSeries.orderTop_add_eq_leftproof · cited by 4
- HahnSeries.min_orderTop_le_orderTop_subproof · cited by 2