[Merged by Bors] - feat(Algebra/Homology): the total complex of a bicomplex #9331
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joelriou
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Dec 29, 2023
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joelriou
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- depends on: [Merged by Bors] - refactor(Algebra/Homology): the category of bicomplexes #9333
- depends on: [Merged by Bors] - feat(Algebra/Homology): signs for the construction of the total complex #9335
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| exact h₁₂ (by simpa only [← h, ← h₂] using ComplexShape.rel_π₂ c₁ c₁₂ i₁ h₁) | ||
| · exact d₂_eq_zero _ _ _ _ _ h₁ | ||
| simp only [GradedObject.ι_descMapObj, comp_zero, w₁, w₂, add_zero] | ||
| d_comp_d' i₁₂ i₁₂' i₁₂'' h₁ h₂ := by |
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This proof is massive. Do you think you can factor out some parts, and possibly deduplicate a bit?
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Thanks for the review! In the last commit 2f17fe7 I have added definitions D₁ and D₂, so that the differential is d := D₁ + D₂, and in order to prove d_comp_d, I have obtained separate lemmas D₁_D₁, D₂_D₁ and D₂_D₂. The code is then slightly longer, but appears in smaller chunks; overall, it should be more manageable. (I also believe that introducing these definitions D₁ and D₂ will ease certain future developments.)
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