Theorems · Definition · field theory

ConditionallyCompleteLinearOrderedField.inducedOrderRingIso

(β : Type u_3) →
  (γ : Type u_4) →
    [inst : Field β] →
      [inst_1 : ConditionallyCompleteLinearOrder β] →
        [IsStrictOrderedRing β] →
          [inst_3 : Field γ] → [inst_4 : ConditionallyCompleteLinearOrder γ] → [IsStrictOrderedRing γ] → β ≃+*o γ

The isomorphism of ordered rings between two conditionally complete linearly ordered fields.

Defined in

Mathlib.Algebra.Order.CompleteField

Cited by

6 results in Mathlib

Foundations

Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldConditionallyCompleteLinearOrderIsStrictOrderedRingFieldConditionallyCompleteLinearOrderIsStrictOrderedRing