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Theorems · Theorem · real analysis

CauSeq.const_sub

∀ {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
3 results in Mathlib
Foundations
Depth 59 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.const_lt · cited by 5CauSeq.const_ltCauSeq.const_equiv · cited by 3CauSeq.const_equivCauSeq.Completion.ofRat_sub · cited by 0Completion.ofRat_subLinearOrder · cited by 8572LinearOrderRing · cited by 7463RingField · cited by 7404FieldIsStrictOrderedRing · cited by 2490IsStrictOrderedRingCauSeq · cited by 189CauSeqIsAbsoluteValue · cited by 160IsAbsoluteValueCauSeq.const · cited by 58CauSeq.constCauSeq.const_subCITED BYCITES

Cites7

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

Cited by3

Results whose statement or proof uses this declaration.