Algebra.lean`

Explanation legend Lean4 Domain Explanation Language (L4DEL)

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L4DEL: Lean4 Domain Explanation Language

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2 declarations, 0 contain sorry, 0 declared as axioms

Algebra

Material destined for Mathlib.

Imports (2)

Imported by 3 files

def AlgHom.rTensor The base extension of an R-algebra homomorphism f : N → P to an f-semilinear map N ⊗[R] M → P ⊗[R] M line 24 source
Source documentation
The base extension of an R-algebra homomorphism f : N → P to an f-semilinear map N ⊗[R] M → P ⊗[R] M.

standard axioms: Quot.sound, propext what this means
Statement uses: CommSemiring, AddCommMonoid, Semiring, Module, Algebra, AlgHom, LinearMap, AlgHom.toRingHom, TensorProduct
Proof uses: RingHom.id, LinearMap.rTensor, LinearMap.mk, LinearMap.toAddHom
20 instances, coercions and auxiliary constants left out.

Tactic trace: 9 steps
Open to load the checked before-and-after goal states.
```
def AlgHom.rTensor {R : Type*} [CommSemiring R] (M : Type*) {N : Type*}
    {P : Type*} [AddCommMonoid M] [Semiring N] [Semiring P] [Module R M]
    [Algebra R N] [Algebra R P] (f : N →ₐ[R] P) :
  N ⊗[R] M →ₛₗ[f.toRingHom] P ⊗[R] M := {
…
```
lemma AlgHom.rTensor_map_smul line 42 source
standard axioms: Quot.sound, propext what this means
Statement uses: CommSemiring, AddCommMonoid, Semiring, Module, Algebra, AlgHom, TensorProduct, Eq, LinearMap, AlgHom.toRingHom, AlgHom.rTensor, HSMul.hSMul
Proof uses: MulActionHom.map_smul', RingHom, LinearMap.toMulActionHom
33 instances, coercions and auxiliary constants left out.