Theorems · Theorem · commutative algebra

TensorProduct.induction_on

∀ {R : Type u_1} [inst : CommSemiring R] {M : Type u_7} {N : Type u_8} [inst_1 : AddCommMonoid M]
  [inst_2 : AddCommMonoid N] [inst_3 : Module R M] [inst_4 : Module R N] {motive : TensorProduct R M N → Prop}
  (z : TensorProduct R M N),
  motive 0 →
    (∀ (x : M) (y : N), motive (x ⊗ₜ[R] y)) →
      (∀ (x y : TensorProduct R M N), motive x → motive y → motive (x + y)) → motive z

Defined in

Mathlib.LinearAlgebra.TensorProduct.Defs

Cited by

81 results in Mathlib

Foundations

Depth 42 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringAddCommMonoidAddCommMonoidModuleModule