leanprover-community / leanprover-community/mathlib4

Add `Trans` instances for morphisms

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Description

As an example:

import Mathlib.Algebra.Module.Equiv

variables (R A B C D : Type _) [Semiring R] [AddCommMonoid A] [AddCommMonoid B] [AddCommMonoid C] [AddCommMonoid D]
   [Module R A] [Module R B] [Module R C] [Module R D] 

-- TODO: semilinearize
instance : Trans
  -- all but the last two arguments of `LinearEquiv`
  (@LinearEquiv R R _ _ (RingHom.id _) (RingHom.id _) _ _ A B _ _)
  (@LinearEquiv R R _ _ (RingHom.id _) (RingHom.id _) _ _ B C _ _)
  (@LinearEquiv R R _ _ (RingHom.id _) (RingHom.id _) _ _ A C _ _) where trans := LinearEquiv.trans

example (R A B C D : Type _) [Semiring R] [AddCommMonoid A] [AddCommMonoid B] [AddCommMonoid C] [AddCommMonoid D]
   [Module R A] [Module R B] [Module R C] [Module R D] (f : A ≃ₗ[R] B) (g : B ≃ₗ[R] C) (h : C ≃ₗ[R] D) : A ≃ₗ[R] D := by
  calc
    A ≃ₗ[R] B := f
    B ≃ₗ[R] C := g
    C ≃ₗ[R] D := h

We already have this for Equiv

We should have it for at least:

  • (Add)MonoidHom
  • RingHom
  • LinearMap
  • AlgHom
  • AddEquiv/MulEquiv
  • RingEquiv
  • LinearEquiv
  • AlgEquiv

Contributor guide

Open the contributing guide

First steps

  1. Read the whole issue, then the project's contributing guide.
  2. Comment on the issue to say you are picking it up — it saves two people doing the same work.
  3. Fork the repository and make your change on a branch.
  4. Open a pull request that references the issue number.

Research direction

Start with the existing Trans instance for Equiv and the example importing Mathlib.Algebra.Module.Equiv. Review the listed morphism types—(Add)MonoidHom, RingHom, LinearMap, AlgHom, AddEquiv, MulEquiv, RingEquiv, LinearEquiv, and AlgEquiv—and add the corresponding instances so the chained calc example works for each applicable type.

Written by the indexing model from the issue text.

Assessment

Domain
tooling
Issue type
Feature
Difficulty
4/5
Estimated time
3-5 days
Activity status
Stale
Clarity
Mostly clear
Newbie friendliness
35/100

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