[Merged by Bors] - feat(linear_algebra/{multilinear,alternating): add of_subsingleton #9196
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This was refactored from the `koszul_cx` branch, something I mentioned doing in [this Zulip thread](https://leanprover.zulipchat.com/#narrow/stream/113488-general/topic/two.20decidable_eq.20instances.20on.20.28fin.201.29.20in.20mathlib.20.3A-.28/near/225596630). The original version was: ```lean def multilinear_map.of_subsingleton (ι : Type v) [subsingleton ι] [inhabited ι] {N : Type u} [add_comm_group N] [module R N] (f : M →ₗ[R] N) : multilinear_map R (λ (i : ι), M) N := { to_fun := λ x, f (x $ default ι), map_add' := λ m i x y, by rw subsingleton.elim i (default ι); simp only [function.update_same, f.map_add], map_smul' := λ m i r x, by rw subsingleton.elim i (default ι); simp only [function.update_same, f.map_smul], } ``` but I decided to remove the `f : M →ₗ[R] N` argument as it can be added later with `(of_subsingleton R M i).comp_linear_map f`. Co-authored-by: Amelia Livingston <al3717@ic.ac.uk>
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…9196) This was refactored from the `koszul_cx` branch, something I mentioned doing in [this Zulip thread](https://leanprover.zulipchat.com/#narrow/stream/113488-general/topic/two.20decidable_eq.20instances.20on.20.28fin.201.29.20in.20mathlib.20.3A-.28/near/225596630). The original version was: ```lean def multilinear_map.of_subsingleton (ι : Type v) [subsingleton ι] [inhabited ι] {N : Type u} [add_comm_group N] [module R N] (f : M →ₗ[R] N) : multilinear_map R (λ (i : ι), M) N := { to_fun := λ x, f (x $ default ι), map_add' := λ m i x y, by rw subsingleton.elim i (default ι); simp only [function.update_same, f.map_add], map_smul' := λ m i r x, by rw subsingleton.elim i (default ι); simp only [function.update_same, f.map_smul], } ``` but I decided to remove the `f : M →ₗ[R] N` argument as it can be added later with `(of_subsingleton R M i).comp_linear_map f`. Co-authored-by: Amelia Livingston <al3717@ic.ac.uk>
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This was refactored from the
koszul_cxbranch, something I mentioned doing in this Zulip thread.The original version was:
but I decided to remove the
f : M →ₗ[R] Nargument as it can be added later with(of_subsingleton R M i).comp_linear_map f.Co-authored-by: Amelia Livingston al3717@ic.ac.uk
Link to the original:
mathlib/src/m4r/Koszul_eq_free_Koszul.lean
Lines 80 to 86 in df4221e