Theorems · Theorem · order theory
ArchimedeanClass.pos_of_pos_of_mk_lt
∀ {M : Type u_1} [inst : AddCommGroup M] [inst_1 : LinearOrder M] [inst_2 : IsOrderedAddMonoid M] {a b : M},
0 < a → ArchimedeanClass.mk a < ArchimedeanClass.mk (b - a) → 0 < b- Defined in
- Mathlib.Algebra.Order.Archimedean.Class
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- LinearOrderstatement and proof · cited by 8,572
- LT.lt.leproof · cited by 2,189
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- ArchimedeanClassstatement · cited by 247
- ArchimedeanClass.mkstatement and proof · cited by 174
- ArchimedeanClass.mk_negproof · cited by 15
- Left.neg_nonpos_iffproof · cited by 14
- lt_add_iff_pos_rightproof · cited by 13
- ArchimedeanClass.lt_of_mk_lt_mk_of_nonposproof · cited by 6
- neg_lt_sub_iff_lt_addproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- HahnEmbedding.Seed.baseEmbedding_posproof · cited by 1