Theorems · Theorem · order theory
ArchimedeanClass.mk_sub_comm
∀ {M : Type u_1} [inst : AddCommGroup M] [inst_1 : LinearOrder M] [inst_2 : IsOrderedAddMonoid M] (a b : M),
ArchimedeanClass.mk (a - b) = ArchimedeanClass.mk (b - a)- Defined in
- Mathlib.Algebra.Order.Archimedean.Class
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- neg_subproof · cited by 272
- ArchimedeanClassstatement and proof · cited by 247
- ArchimedeanClass.mkstatement and proof · cited by 174
- ArchimedeanClass.mk_negproof · cited by 15
Cited by4
Results whose statement or proof uses this declaration.
- ArchimedeanClass.mk_right_le_mk_sub_iffproof · cited by 1
- HahnEmbedding.Partial.eval_ltproof · cited by 1
- HahnEmbedding.Seed.baseEmbedding_posproof · cited by 1
- HahnEmbedding.Partial.archimedeanClassMk_le_of_eval_eqproof · cited by 1