Skip to content

Commit

Permalink
.
Browse files Browse the repository at this point in the history
  • Loading branch information
kim-em committed Nov 23, 2024
1 parent 0e3bc99 commit 7e552ce
Showing 1 changed file with 0 additions and 22 deletions.
22 changes: 0 additions & 22 deletions Mathlib/LinearAlgebra/Multilinear/Basic.lean
Original file line number Diff line number Diff line change
Expand Up @@ -1719,7 +1719,6 @@ theorem curryFinFinset_symm_apply {k l n : ℕ} {s : Finset (Fin n)} (hk : #s =
m <| finSumEquivOfFinset hk hl (Sum.inr i) :=
rfl

-- @[simp] -- Porting note: simpNF linter, lhs simplifies, added aux version below
theorem curryFinFinset_symm_apply_piecewise_const {k l n : ℕ} {s : Finset (Fin n)} (hk : #s = k)
(hl : #sᶜ = l)
(f : MultilinearMap R (fun _ : Fin k => M') (MultilinearMap R (fun _ : Fin l => M') M₂))
Expand All @@ -1734,26 +1733,13 @@ theorem curryFinFinset_symm_apply_piecewise_const {k l n : ℕ} {s : Finset (Fin
rw [finSumEquivOfFinset_inr, Finset.piecewise_eq_of_not_mem]
exact Finset.mem_compl.1 (Finset.orderEmbOfFin_mem _ _ _)

@[simp]
theorem curryFinFinset_symm_apply_piecewise_const_aux {k l n : ℕ} {s : Finset (Fin n)}
(hk : #s = k) (hl : #sᶜ = l)
(f : MultilinearMap R (fun _ : Fin k => M') (MultilinearMap R (fun _ : Fin l => M') M₂))
(x y : M') :
((⇑f fun _ => x) (fun i => (Finset.piecewise s (fun _ => x) (fun _ => y)
((sᶜ.orderEmbOfFin hl) i))) = f (fun _ => x) fun _ => y) := by
have := curryFinFinset_symm_apply_piecewise_const hk hl f x y
simp only [curryFinFinset_symm_apply, finSumEquivOfFinset_inl, Finset.orderEmbOfFin_mem,
Finset.piecewise_eq_of_mem, finSumEquivOfFinset_inr] at this
exact this

@[simp]
theorem curryFinFinset_symm_apply_const {k l n : ℕ} {s : Finset (Fin n)} (hk : #s = k)
(hl : #sᶜ = l)
(f : MultilinearMap R (fun _ : Fin k => M') (MultilinearMap R (fun _ : Fin l => M') M₂))
(x : M') : ((curryFinFinset R M₂ M' hk hl).symm f fun _ => x) = f (fun _ => x) fun _ => x :=
rfl

-- @[simp] -- Porting note: simpNF, lhs simplifies, added aux version below
theorem curryFinFinset_apply_const {k l n : ℕ} {s : Finset (Fin n)} (hk : #s = k)
(hl : #sᶜ = l) (f : MultilinearMap R (fun _ : Fin n => M') M₂) (x y : M') :
(curryFinFinset R M₂ M' hk hl f (fun _ => x) fun _ => y) =
Expand All @@ -1762,14 +1748,6 @@ theorem curryFinFinset_apply_const {k l n : ℕ} {s : Finset (Fin n)} (hk : #s =
refine (curryFinFinset_symm_apply_piecewise_const hk hl _ _ _).symm.trans ?_
rw [LinearEquiv.symm_apply_apply]

@[simp]
theorem curryFinFinset_apply_const_aux {k l n : ℕ} {s : Finset (Fin n)} (hk : #s = k)
(hl : #sᶜ = l) (f : MultilinearMap R (fun _ : Fin n => M') M₂) (x y : M') :
(f fun i => Sum.elim (fun _ => x) (fun _ => y) ((⇑ (Equiv.symm (finSumEquivOfFinset hk hl))) i))
= f (s.piecewise (fun _ => x) fun _ => y) := by
rw [← curryFinFinset_apply]
apply curryFinFinset_apply_const

end MultilinearMap

end Currying
Expand Down

0 comments on commit 7e552ce

Please sign in to comment.