Theorems · Theorem · ring theory

IsSymmetricAlgebra.induction

∀ {R : Type u_1} {M : Type u_2} [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {A : Type u_3}
  [inst_3 : CommSemiring A] [inst_4 : Algebra R A] {f : M →ₗ[R] A},
  IsSymmetricAlgebra f →
    ∀ {motive : A → Prop},
      (∀ (r : R), motive ((algebraMap R A) r)) →
        (∀ (x : M), motive (f x)) →
          (∀ (a b : A), motive a → motive b → motive (a * b)) →
            (∀ (a b : A), motive a → motive b → motive (a + b)) → ∀ (a : A), motive a

Defined in

Mathlib.LinearAlgebra.SymmetricAlgebra.Basic

Cited by

0 results in Mathlib

Foundations

Depth 55 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringAddCommMonoidModuleCommSemiringAlgebra