[Merged by Bors] - feat(linear_algebra/free_module/ideal_quotient): add ideal.finrank_quotient_eq_sum #19084
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Part of the auxiliary file in #18000 |
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Co-authored-by: Junyan Xu <junyanxumath@gmail.com>
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| lemma ideal.finrank_quotient_eq_sum [nontrivial F] | ||
| [∀ i, module.free F (R ⧸ ideal.span ({I.smith_coeffs b hI i} : set R))] | ||
| [∀ i, module.finite F (R ⧸ ideal.span ({I.smith_coeffs b hI i} : set R))] : | ||
| finite_dimensional.finrank F (S ⧸ I) | ||
| = ∑ i, finite_dimensional.finrank F (R ⧸ ideal.span ({I.smith_coeffs b hI i} : set R)) := | ||
| begin | ||
| rw [linear_equiv.finrank_eq $ ideal.quotient_equiv_direct_sum F b hI, | ||
| finite_dimensional.finrank_direct_sum] | ||
| -- slow, and dot notation doesn't work | ||
| end |
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This lemma might look unnecessary but I just tested and it can't be inlined in finrank_quotient_span_eq_nat_degree_norm in #18000.
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Thanks! bors merge |
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…otient_eq_sum (#19084) Co-authored-by: Junyan Xu <junyanxumath@gmail.com>
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@Multramate, before you make many more mathlib3 PRs, please forward-port this and your other four changes (two PRs) on https://leanprover-community.github.io/mathlib-port-status/out-of-sync |
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| instance (F : Type u) [comm_ring F] [algebra F R] (b : basis ι R S) {I : ideal S} (hI : I ≠ ⊥) (i) : | ||
| module F (R ⧸ ideal.span ({I.smith_coeffs b hI i} : set R)) := | ||
| by apply_instance -- quotient.module' _ | ||
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What was the purpose of adding this instance if apply_instance can already find it?
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See #19084 (comment)
It's weird we need to add a shortcut instance that is already found by typeclass inference.
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…4821) [`linear_algebra.free_module.ideal_quotient`@`6623e6af705e97002a9054c1c05a980180276fc1`..`d87199d51218d36a0a42c66c82d147b5a7ff87b3`](https://leanprover-community.github.io/mathlib-port-status/file/linear_algebra/free_module/ideal_quotient?range=6623e6af705e97002a9054c1c05a980180276fc1..d87199d51218d36a0a42c66c82d147b5a7ff87b3)
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…4820) [`linear_algebra.free_module.pid`@`210657c4ea4a4a7b234392f70a3a2a83346dfa90`..`d87199d51218d36a0a42c66c82d147b5a7ff87b3`](https://leanprover-community.github.io/mathlib-port-status/file/linear_algebra/free_module/pid?range=210657c4ea4a4a7b234392f70a3a2a83346dfa90..d87199d51218d36a0a42c66c82d147b5a7ff87b3) Co-authored-by: Junyan Xu <junyanxu.math@gmail.com>
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…eanprover-community#4821) [`linear_algebra.free_module.ideal_quotient`@`6623e6af705e97002a9054c1c05a980180276fc1`..`d87199d51218d36a0a42c66c82d147b5a7ff87b3`](https://leanprover-community.github.io/mathlib-port-status/file/linear_algebra/free_module/ideal_quotient?range=6623e6af705e97002a9054c1c05a980180276fc1..d87199d51218d36a0a42c66c82d147b5a7ff87b3)
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…eanprover-community#4820) [`linear_algebra.free_module.pid`@`210657c4ea4a4a7b234392f70a3a2a83346dfa90`..`d87199d51218d36a0a42c66c82d147b5a7ff87b3`](https://leanprover-community.github.io/mathlib-port-status/file/linear_algebra/free_module/pid?range=210657c4ea4a4a7b234392f70a3a2a83346dfa90..d87199d51218d36a0a42c66c82d147b5a7ff87b3) Co-authored-by: Junyan Xu <junyanxu.math@gmail.com>
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Co-authored-by: Junyan Xu junyanxumath@gmail.com