English
Equality of multilinear maps follows from equality on structured inputs via a basis decomposition.
Русский
Равенство много-линейных отображений следует из равенства на структурированных вводах через разложение по базису.
LaTeX
$$If for all input vectors the outputs coincide, then the multilinear maps are equal.$$
Lean4
/-- Given a linear map `f` from `M 0` to multilinear maps on `n` variables,
construct the corresponding multilinear map on `n+1` variables obtained by concatenating
the variables, given by `m ↦ f (m 0) (tail m)` -/
def uncurryLeft (f : M 0 →ₗ[R] MultilinearMap R (fun i : Fin n => M i.succ) M₂) : MultilinearMap R M M₂ :=
MultilinearMap.mk' (fun m ↦ f (m 0) (tail m)) (fun m i x y ↦ by cases i using Fin.cases <;> simp [Ne.symm])
(fun m i c x ↦ by cases i using Fin.cases <;> simp [Ne.symm])
