[Merged by Bors] - feat(RingTheory/Finiteness): Improve fg_induction#37484
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martinwintermath wants to merge 4 commits intoleanprover-community:masterfrom
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[Merged by Bors] - feat(RingTheory/Finiteness): Improve fg_induction#37484martinwintermath wants to merge 4 commits intoleanprover-community:masterfrom
fg_induction#37484martinwintermath wants to merge 4 commits intoleanprover-community:masterfrom
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PR summary e5c478fa82Import changes for modified filesNo significant changes to the import graph Import changes for all files
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Thanks for fixing this. Could you please mention the fact that this change enables usage of induction with this lemma in the PR description?
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- include the FG-hypothesis into motive for `fg_induction`. This is necessary, since it might be that `P (M₁ ⊔ M₂)` is only provable from `P M₁`and `P M₂` if we can use that `M₁` and `M₂` are FG. Also, `M₁.FG` and `M₂.FG` are not provable from `(M₁ ⊔ M₂).FG` in general. This also enables the use of the `induction` tactic with `fg_induction`. - add `fg_sup_span_induction` that adds one 1-dimensional submodule at a time. - give expressive names to the induction start and induction step hypotheses. Co-authored-by: Martin Winter <martin.winter.math@gmail.com>
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fg_inductionfg_induction
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fg_induction. This is necessary, since it might be thatP (M₁ ⊔ M₂)is only provable fromP M₁andP M₂if we can use thatM₁andM₂are FG. Also,M₁.FGandM₂.FGare not provable from(M₁ ⊔ M₂).FGin general. This also enables the use of theinductiontactic withfg_induction.fg_sup_span_inductionthat adds one 1-dimensional submodule at a time.