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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
Assumes
AddCommGroupLinearOrderIsOrderedAddMonoid

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

ArchimedeanClass.stdPart_neg · cited by 5ArchimedeanClass.stdPart_…ArchimedeanClass.mk_sub_comm · cited by 4ArchimedeanClass.mk_sub_c…ArchimedeanClass.lt_of_stdPart_lt · cited by 2ArchimedeanClass.lt_of_st…ArchimedeanClass.mk_left_le_mk_add_iff · cited by 2ArchimedeanClass.mk_left_…ArchimedeanClass.mk_left_le_mk_sub · cited by 2ArchimedeanClass.mk_left_…ArchimedeanClass.exists_int_lt_of_mk_nonneg · cited by 1ArchimedeanClass.exists_i…ArchimedeanClass.min_le_mk_sub · cited by 1ArchimedeanClass.min_le_m…ArchimedeanClass.pos_of_pos_of_mk_lt · cited by 1ArchimedeanClass.pos_of_p…ArchimedeanClass.exists_int_le_of_mk_nonneg · cited by 0ArchimedeanClass.exists_i…ArchimedeanClass.mk_sub_eq_mk_left · cited by 0ArchimedeanClass.mk_sub_e…ArchimedeanClass.mk_sub_eq_mk_right · cited by 0ArchimedeanClass.mk_sub_e…FiniteArchimedeanClass.mk_neg · cited by 0FiniteArchimedeanClass.mk…ArchimedeanClass.stdPart_sub · cited by 0ArchimedeanClass.stdPart_…ArchimedeanClass.stdPart_sub_eq_left · cited by 0ArchimedeanClass.stdPart_…ArchimedeanClass.mk_right_le_mk_sub · cited by 0ArchimedeanClass.mk_right…AddCommGroup · cited by 12871AddCommGroupLinearOrder · cited by 8572LinearOrderabs · cited by 1814absIsOrderedAddMonoid · cited by 1659IsOrderedAddMonoidArchimedeanClass · cited by 247ArchimedeanClassArchimedeanClass.mk · cited by 174ArchimedeanClass.mkabs_neg · cited by 93abs_negone_nsmul · cited by 63one_nsmulArchimedeanClass.mk_eq_mk · cited by 8ArchimedeanClass.mk_eq_mkArchimedeanClass.mk_negCITED BYCITES

Cites9

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by15

Results whose statement or proof uses this declaration.