Theorems · Theorem · order theory
FiniteArchimedeanClass.min_le_mk_add
∀ {M : Type u_1} [inst : AddCommGroup M] [inst_1 : LinearOrder M] [inst_2 : IsOrderedAddMonoid M] {a b : M} (ha : a ≠ 0)
(hb : b ≠ 0) (hab : a + b ≠ 0),
min (FiniteArchimedeanClass.mk a ha) (FiniteArchimedeanClass.mk b hb) ≤ FiniteArchimedeanClass.mk (a + b) hab- Defined in
- Mathlib.Algebra.Order.Archimedean.Class
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommGroupstatement and proof · cited by 12,871
- Top.topstatement · cited by 9,680
- LinearOrderstatement and proof · cited by 8,572
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- ArchimedeanClassstatement · cited by 247
- FiniteArchimedeanClassstatement · cited by 100
- FiniteArchimedeanClass.mkstatement · cited by 28
- ArchimedeanClass.min_le_mk_addproof · cited by 5
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