Theorems · Theorem · commutative algebra

IsTensorProduct.inductionOn

∀ {R : Type u_1} [inst : CommSemiring R] {M₁ : Type u_2} {M₂ : Type u_3} {M : Type u_4} [inst_1 : AddCommMonoid M₁]
  [inst_2 : AddCommMonoid M₂] [inst_3 : AddCommMonoid M] [inst_4 : Module R M₁] [inst_5 : Module R M₂]
  [inst_6 : Module R M] {f : M₁ →ₗ[R] M₂ →ₗ[R] M},
  IsTensorProduct f →
    ∀ {motive : M → Prop} (m : M),
      motive 0 →
        (∀ (x : M₁) (y : M₂), motive ((f x) y)) → (∀ (x y : M), motive x → motive y → motive (x + y)) → motive m

Defined in

Mathlib.RingTheory.IsTensorProduct

Cited by

8 results in Mathlib

Foundations

Depth 59 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringAddCommMonoidAddCommMonoidAddCommMonoidModuleModuleModule