Theorems · Theorem · field theory

ConditionallyCompleteLinearOrderedField.le_inducedMap_mul_self_of_mem_cutMap

∀ {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] {a : α},
  0 < a →
    ∀ b ∈ LinearOrderedField.cutMap β (a * a),
      b ≤
        ConditionallyCompleteLinearOrderedField.inducedMap α β a *
          ConditionallyCompleteLinearOrderedField.inducedMap α β a

Preparatory lemma for inducedOrderRingHom.

Defined in

Mathlib.Algebra.Order.CompleteField

Cited by

1 results in Mathlib

Foundations

Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldLinearOrderIsStrictOrderedRingFieldConditionallyCompleteLinearOrderIsStrictOrderedRingArchimedean