FiniteFree.lean`

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1 declarations, 0 contain sorry, 0 declared as axioms

Finite Free

Material destined for Mathlib.

Imports (2)

Imported by 2 files

def LinearEquiv.chooseBasisPiScalarRight The M-algebra isomorphism M ⊗ V ≃ₗ[M] (ι → M) coming from the canonical ι-indexed basis of a finite free R-module V line 25 source
Source documentation
The M-algebra isomorphism M ⊗ V ≃ₗ[M] (ι → M) coming from the canonical ι-indexed basis of a finite free R-module V.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: CommSemiring, CommRing, Algebra, AddCommGroup, Module, Module.Finite, Module.Free, LinearEquiv, RingHom.id, TensorProduct, Module.Free.ChooseBasisIndex
Proof uses: LinearEquiv.trans, LinearEquiv.baseChange, Module.Basis.equivFun, Module.Free.chooseBasis, TensorProduct.piScalarRight
31 instances, coercions and auxiliary constants left out.

Tactic trace: 4 steps
Open to load the checked before-and-after goal states.
```
noncomputable def LinearEquiv.chooseBasisPiScalarRight (R : Type*) (M : Type*) (V : Type*)
    -- Probably OK for Semirings?
    -- commutativity needed in the below construction for `TensorProduct.piScalarRight`
    [CommSemiring M] [CommRing R] [Algebra R M]
    [AddCommGroup V] [Module R V] [Module.Finite R V] [Module.Free R V] :
    (M ⊗[R] V) ≃ₗ[M] (Module.Free.ChooseBasisIndex R V → M) := by
…
```