Theorems · Theorem · order theory
ArchimedeanClass.mk_neg
∀ {M : Type u_1} [inst : AddCommGroup M] [inst_1 : LinearOrder M] [inst_2 : IsOrderedAddMonoid M] (a : M),
ArchimedeanClass.mk (-a) = ArchimedeanClass.mk a- Defined in
- Mathlib.Algebra.Order.Archimedean.Class
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- absproof · cited by 1,814
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- ArchimedeanClassstatement · cited by 247
- ArchimedeanClass.mkstatement · cited by 174
- abs_negproof · cited by 93
- one_nsmulproof · cited by 63
- ArchimedeanClass.mk_eq_mkproof · cited by 8
Cited by15
Results whose statement or proof uses this declaration.
- ArchimedeanClass.stdPart_negproof · cited by 5
- ArchimedeanClass.mk_sub_commproof · cited by 4
- ArchimedeanClass.lt_of_stdPart_ltproof · cited by 2
- ArchimedeanClass.mk_left_le_mk_add_iffproof · cited by 2
- ArchimedeanClass.mk_left_le_mk_subproof · cited by 2
- ArchimedeanClass.exists_int_lt_of_mk_nonnegproof · cited by 1
- ArchimedeanClass.min_le_mk_subproof · cited by 1
- ArchimedeanClass.pos_of_pos_of_mk_ltproof · cited by 1
- ArchimedeanClass.exists_int_le_of_mk_nonnegproof · cited by 0
- ArchimedeanClass.mk_sub_eq_mk_leftproof · cited by 0
- ArchimedeanClass.mk_sub_eq_mk_rightproof · cited by 0
- FiniteArchimedeanClass.mk_negproof · cited by 0