feat(data/dfinsupp): Add an equivalence between (Π₀ i j, β i j) and (Π₀ ij, β ij.1 ij.2) #3515
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…Π₀ ij, β ij.1 ij.2) This is very much a work in progress. Submitting this commit so others can try and flesh out the proofs.
eric-wieser
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eric-wieser
commented
Jul 22, 2020
eric-wieser
commented
Jul 22, 2020
src/data/dfinsupp/prod.lean
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| let js : multiset jj := quotient.lift_on (fi.to_fun i) | ||
| dfinsupp.pre.pre_support | ||
| (λ a b H, begin | ||
| /- This is unprovable, I think lift_on is the wrong approach, or I need to return a clever quotient -/ | ||
| sorry | ||
| end), |
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an alternative is to invoke the axiom of choice:
Suggested change
| let js : multiset jj := quotient.lift_on (fi.to_fun i) | |
| dfinsupp.pre.pre_support | |
| (λ a b H, begin | |
| /- This is unprovable, I think lift_on is the wrong approach, or I need to return a clever quotient -/ | |
| sorry | |
| end), | |
| let js : multiset jj := dfinsupp.pre.pre_support (quotient.out (fi.to_fun i)), |
but that still makes the following sorry hard to prove.
pbazin
reviewed
Apr 1, 2022
| exact ⟦{ | ||
| to_fun := λ i, ⟦ { | ||
| to_fun := λ j, fij.to_fun (i, j), | ||
| pre_support := fij.pre_support.map prod.snd, |
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well this doesn't transfer easily when replacing ι₁ × ι₂ by a sigma type
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I had assumed it would be fine, but the comment you made in the other PR looked convincing
|
Closed in favor of #18316. |
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equiv.Pi_curry/finsupp_prod_equiv, but fordfinsupp.Unlike
finsupp_prod_equivin 92b9a00, this aims to not require[add_comm_monoid _]This is very much a work in progress. Submitting this commit so others can try and flesh out the proofs.