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Theorems · Theorem · real analysis

CauSeq.const_mul

∀ {α : Type u_1} {β : Type u_2} [inst : Field α] [inst_1 : LinearOrder α] [inst_2 : IsStrictOrderedRing α]
  [inst_3 : Ring β] {abv : β → α} [inst_4 : IsAbsoluteValue abv] (x y : β),
  CauSeq.const abv (x * y) = CauSeq.const abv x * CauSeq.const abv y
Defined in
Mathlib.Algebra.Order.CauSeq.Basic
Cited by
1 results in Mathlib
Foundations
Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FieldLinearOrderIsStrictOrderedRingRingIsAbsoluteValue
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Around this declaration

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

CauSeq.Completion.ofRat_mul · cited by 1Completion.ofRat_mulLinearOrder · cited by 8572LinearOrderRing · cited by 7463RingField · cited by 7404FieldIsStrictOrderedRing · cited by 2490IsStrictOrderedRingCauSeq · cited by 189CauSeqIsAbsoluteValue · cited by 160IsAbsoluteValueCauSeq.const · cited by 58CauSeq.constCauSeq.const_mulCITED BYCITES

Cites7

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Cited by1

Results whose statement or proof uses this declaration.