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Theorems · Theorem · order theory

ArchimedeanClass.mk_mul

∀ {R : Type u_1} [inst : LinearOrder R] [inst_1 : CommRing R] [inst_2 : IsStrictOrderedRing R] (x y : R),
  ArchimedeanClass.mk (x * y) = ArchimedeanClass.mk x + ArchimedeanClass.mk y
Defined in
Mathlib.Algebra.Order.Ring.Archimedean
Cited by
1 results in Mathlib
Foundations
Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
LinearOrderCommRingIsStrictOrderedRing
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Around this declaration

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

ArchimedeanClass.addValuation · cited by 15ArchimedeanClass.addValua…ArchimedeanClass.mk_div · cited by 0ArchimedeanClass.mk_divCommRing · cited by 17173CommRingLinearOrder · cited by 8572LinearOrderIsStrictOrderedRing · cited by 2490IsStrictOrderedRingArchimedeanClass · cited by 247ArchimedeanClassArchimedeanClass.mk · cited by 174ArchimedeanClass.mkArchimedeanClass.mk_mulCITED BYCITES

Cites5

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Cited by2

Results whose statement or proof uses this declaration.