Theorems · Theorem · ring theory

MonoidAlgebra.induction_on

∀ {R : Type u_1} {M : Type u_4} [inst : Semiring R] [inst_1 : Monoid M] {motive : MonoidAlgebra R M → Prop}
  (x : MonoidAlgebra R M),
  (∀ (m : M), motive ((MonoidAlgebra.of R M) m)) →
    (∀ (x y : MonoidAlgebra R M), motive x → motive y → motive (x + y)) →
      (∀ (r : R) (x : MonoidAlgebra R M), motive x → motive (r • x)) → motive x

Defined in

Mathlib.Algebra.MonoidAlgebra.Defs

Cited by

6 results in Mathlib

Foundations

Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringMonoid