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Theorems · Theorem · field theory

LinearOrderedField.inducedMap_zero

Deprecated since 2026-02-24Use ConditionallyCompleteLinearOrderedField.inducedMap_zero instead.

∀ (α : Type u_2) (β : Type u_3) [inst : Field α] [inst_1 : LinearOrder α] [IsStrictOrderedRing α] [inst_3 : Field β]
  [inst_4 : ConditionallyCompleteLinearOrder β] [IsStrictOrderedRing β] [Archimedean α],
  ConditionallyCompleteLinearOrderedField.inducedMap α β 0 = 0

Alias of ConditionallyCompleteLinearOrderedField.inducedMap_zero.

Defined in
Mathlib.Algebra.Order.CompleteField
Cited by
0 results in Mathlib
Foundations
Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FieldLinearOrderIsStrictOrderedRingFieldConditionallyCompleteLinearOrderIsStrictOrderedRingArchimedean
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Around this declaration

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LinearOrder · cited by 8572LinearOrderField · cited by 7404FieldIsStrictOrderedRing · cited by 2490IsStrictOrderedRingArchimedean · cited by 603ArchimedeanConditionallyCompleteLinearOrder · cited by 542ConditionallyCompleteLine…ConditionallyCompleteLinearOrderedField.inducedMap · cited by 28ConditionallyCompleteLine…ConditionallyCompleteLinearOrderedField.inducedMap_zero · cited by 2ConditionallyCompleteLine…LinearOrderedField.inducedMap…CITED BYCITES

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