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feat(Torsion/Basic): Add a few convenient lemmas for torsion submodules#35534

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feat(Torsion/Basic): Add a few convenient lemmas for torsion submodules#35534
xgenereux wants to merge 2 commits intoleanprover-community:masterfrom
xgenereux:sup_torsionBySet_ideal_eq_torsionBySet_inf

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This PR adds a few convenient lemmas in Torsion/Basic.

In particular, it adds:

  • A version of torsionBySet_span_singleton_eq for Ideals. These two are added to the simp set.
  • Show two instances of isTorsionBy/isTorsionBySet being IsTorsion in the form of torsionBy_isTorsion_nonZeroDivisor and torsionBySet_ideal_isTorsion_of_noZeroDivisors.
  • Add a version of iSup_torsionBySet_ideal_eq_torsionBySet_iInf and supIndep_torsionBySet_ideal for sup instead of iSup.

Note: To go from iSup to sup I need to talk about Fin 2 which requires Finset.univ_fin2 that is in Mathlib but in a weird place. I just put it as a have in my proof.

Note2: one could also use {P,Q} and id instead of the map from Fin 2 but that makes the proof of disjoint_torsionBySet_ideal inconvenient.

Co-authored-by: María Inés de Frutos Fernández <mariaines.dff@gmail.com>


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@github-actions github-actions bot added the t-algebra Algebra (groups, rings, fields, etc) label Feb 19, 2026
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github-actions bot commented Feb 19, 2026

PR summary af97ef4b5b

Import changes for modified files

No significant changes to the import graph

Import changes for all files
Files Import difference

Declarations diff

+ disjoint_torsionBySet_ideal
+ sup_torsionBySet_ideal_eq_torsionBySet_inf
+ torsionBySet_ideal_isTorsion_of_noZeroDivisors
+ torsionBySet_ideal_span_singleton_eq
+ torsionBy_isTorsion_nonZeroDivisor

You can run this locally as follows
## summary with just the declaration names:
./scripts/declarations_diff.sh <optional_commit>

## more verbose report:
./scripts/declarations_diff.sh long <optional_commit>

The doc-module for scripts/declarations_diff.sh contains some details about this script.


No changes to technical debt.

You can run this locally as

./scripts/technical-debt-metrics.sh pr_summary
  • The relative value is the weighted sum of the differences with weight given by the inverse of the current value of the statistic.
  • The absolute value is the relative value divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).

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