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Theorems · Theorem · order theory

MulArchimedeanClass.mk_div_lt_mk_left_iff

∀ {M : Type u_1} [inst : CommGroup M] [inst_1 : LinearOrder M] [inst_2 : IsOrderedMonoid M] {a b : M},
  MulArchimedeanClass.mk (a / b) < MulArchimedeanClass.mk a ↔ MulArchimedeanClass.mk b < MulArchimedeanClass.mk a
Defined in
Mathlib.Algebra.Order.Archimedean.Class
Cited by
0 results in Mathlib
Foundations
Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommGroupLinearOrderIsOrderedMonoid
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LinearOrder · cited by 8572LinearOrderCommGroup · cited by 990CommGroupIsOrderedMonoid · cited by 577IsOrderedMonoidMulArchimedeanClass · cited by 81MulArchimedeanClassMulArchimedeanClass.mk · cited by 63MulArchimedeanClass.mkle_iff_le_iff_lt_iff_lt · cited by 25le_iff_le_iff_lt_iff_ltMulArchimedeanClass.mk_left_le_mk_div_iff · cited by 2MulArchimedeanClass.mk_le…MulArchimedeanClass.mk_div_lt…CITED BYCITES

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