Theorems · Definition · commutative algebra

Valuation.HasExtension.casesOn

{R : Type u_1} →
  {A : Type u_2} →
    {ΓR : Type u_3} →
      {ΓA : Type u_4} →
        [inst : CommRing R] →
          [inst_1 : Ring A] →
            [inst_2 : LinearOrderedCommMonoidWithZero ΓR] →
              [inst_3 : LinearOrderedCommMonoidWithZero ΓA] →
                [inst_4 : Algebra R A] →
                  {vR : Valuation R ΓR} →
                    {vA : Valuation A ΓA} →
                      {motive : vR.HasExtension vA → Sort u} →
                        (t : vR.HasExtension vA) →
                          ((val_isEquiv_comap : vR.IsEquiv (Valuation.comap (algebraMap R A) vA)) → motive ⋯) → motive t

Defined in

Mathlib.RingTheory.Valuation.Extension

Cited by

0 results in Mathlib

Foundations

Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingRingLinearOrderedCommMonoidWithZeroLinearOrderedCommMonoidWithZeroAlgebra