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refactor: Some replacement with rfl

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jstoobysmith 2024-10-19 10:34:30 +00:00
parent 48bec8c891
commit 3e1cd363bd
5 changed files with 12 additions and 22 deletions
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20
HepLean/Mathematics/Fin.lean
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@ -112,7 +112,7 @@ lemma succAbove_succAbove_predAboveI (i : Fin n.succ.succ) (j : Fin n.succ) (x :
· rw [Fin.succAbove_of_castSucc_lt _ _ hx2]
nth_rewrite 2 [Fin.succAbove_of_castSucc_lt _ _]
· rw [Fin.succAbove_of_le_castSucc]
· simp [Fin.ext_iff]
· rfl
· exact hx1
· rw [Fin.lt_def] at hx2 ⊢
simp_all
@ -159,7 +159,7 @@ lemma succAbove_succAbove_predAboveI (i : Fin n.succ.succ) (j : Fin n.succ) (x :
rw [Fin.succAbove_of_le_castSucc _ _ hx2]
nth_rewrite 2 [Fin.succAbove_of_le_castSucc]
· rw [Fin.succAbove_of_castSucc_lt]
· simp [Fin.ext_iff]
· rfl
exact Fin.castSucc_lt_succ_iff.mpr hx1
· rw [Fin.le_def] at hx2 ⊢
simp_all
@ -180,11 +180,10 @@ lemma finExtractOne_apply_eq {n : ℕ} (i : Fin n.succ) :
Equiv.sumCongr_apply, Equiv.coe_trans, Equiv.sumComm_apply, Equiv.coe_refl, Fin.isValue]
have h1 :
Fin.cast (finExtractOne.proof_1 i) i = Fin.castAdd ((n - ↑i)) ⟨i.1, lt_add_one i.1⟩ := by
simp [Fin.ext_iff]
rfl
rw [h1, finSumFinEquiv_symm_apply_castAdd]
simp only [Nat.succ_eq_add_one, Sum.map_inl, Function.comp_apply, Fin.isValue]
have h2 : @Fin.mk (↑i + 1) ↑i (lt_add_one i.1) = Fin.natAdd i.val 1 := by
simp [Fin.ext_iff]
have h2 : @Fin.mk (↑i + 1) ↑i (lt_add_one i.1) = Fin.natAdd i.val 1 := rfl
rw [h2, finSumFinEquiv_symm_apply_natAdd]
rfl
@ -202,9 +201,7 @@ lemma finExtractOne_symm_inr {n : ℕ} (i : Fin n.succ) :
· have h1 : (finSumFinEquiv.symm (Fin.cast (finExtractOne.proof_2 i).symm x)) =
Sum.inl ⟨x, hi⟩ := by
rw [← finSumFinEquiv_symm_apply_castAdd]
apply congrArg
ext
simp
rfl
rw [h1]
simp only [Nat.succ_eq_add_one, Equiv.sumAssoc_symm_apply_inr_inl, Sum.map_inl,
Equiv.symm_trans_apply, Equiv.symm_symm, Equiv.sumComm_symm, Equiv.sumComm_apply,
@ -244,7 +241,6 @@ lemma finExtractOne_symm_inl_apply {n : ℕ} (i : Fin n.succ) :
Equiv.symm_symm, Equiv.sumCongr_symm, Equiv.refl_symm, Equiv.sumCongr_apply, Equiv.coe_refl,
Sum.map_inl, id_eq, Equiv.sumAssoc_symm_apply_inl, Equiv.sumComm_symm, Equiv.sumComm_apply,
Sum.swap_inl, finSumFinEquiv_apply_right, finSumFinEquiv_apply_left, finCongr_apply]
ext
rfl
/-- Given an equivalence `Fin n.succ.succ ≃ Fin n.succ.succ`, and an `i : Fin n.succ.succ`,
@ -276,6 +272,8 @@ lemma finExtractOnPermHom_inv (i : Fin n.succ.succ) (σ : Fin n.succ.succ ≃ Fi
simp only [Nat.succ_eq_add_one, Fin.castSucc_mk]
omega
/-- Given an equivalence `Fin n.succ.succ ≃ Fin n.succ.succ`, and an `i : Fin n.succ.succ`,
the equivalence `Fin n.succ ≃ Fin n.succ` obtained by dropping `i` and it's image. -/
def finExtractOnePerm (i : Fin n.succ.succ) (σ : Fin n.succ.succ ≃ Fin n.succ.succ) :
Fin n.succ ≃ Fin n.succ where
toFun x := finExtractOnPermHom i σ x
@ -320,9 +318,7 @@ lemma finExtractTwo_symm_inl_inr_apply {n : ℕ} (i : Fin n.succ.succ) (j : Fin
@[simp]
lemma finExtractTwo_symm_inl_inl_apply {n : ℕ} (i : Fin n.succ.succ) (j : Fin n.succ) :
(finExtractTwo i j).symm (Sum.inl (Sum.inl 0)) = i := by
rw [finExtractTwo]
simp
(finExtractTwo i j).symm (Sum.inl (Sum.inl 0)) = i := by rfl
@[simp]
lemma finExtractTwo_apply_snd {n : ℕ} (i : Fin n.succ.succ) (j : Fin n.succ) :