simp [k'', ki, kj]
n first last : Nat
α✝ : Type
arr1 arr2 arr✝ arr'✝ : Vec α✝ n
i j : Fin n
fi : first ≤ ↑i
ij : i ≤ j
jl : ↑j ≤ last
p : permuted n first last (arr✝.swap i j) arr'✝
ih : ∀ (k : Fin n), first ≤ ↑k → ↑k ≤ last → ∃ k', p.to_map k' = k ∧ first ≤ ↑k' ∧ ↑k' ≤ last
k : Fin n
fk : first ≤ ↑k
kl : ↑k ≤ last
k' : Fin n
index : p.to_map k' = k
fk' : first ≤ ↑k'
kl' : ↑k' ≤ last
k'' : Fin n := if k' = i then j else if k' = j then i else k'
this : (if k'' = i then j else if k'' = j then i else k'') = k'
ki : ¬k' = i
kj : ¬k' = j
⊢ first ≤ ↑k'' ∧ ↑k'' ≤ last
n first last : Nat
α✝ : Type
arr1 arr2 arr✝ arr'✝ : Vec α✝ n
i j : Fin n
fi : first ≤ ↑i
ij : i ≤ j
jl : ↑j ≤ last
p : permuted n first last (arr✝.swap i j) arr'✝
ih : ∀ (k : Fin n), first ≤ ↑k → ↑k ≤ last → ∃ k', p.to_map k' = k ∧ first ≤ ↑k' ∧ ↑k' ≤ last
k : Fin n
fk : first ≤ ↑k
kl : ↑k ≤ last
k' : Fin n
index : p.to_map k' = k
fk' : first ≤ ↑k'
kl' : ↑k' ≤ last
k'' : Fin n := if k' = i then j else if k' = j then i else k'
this : (if k'' = i then j else if k'' = j then i else k'') = k'
ki : ¬k' = i
kj : ¬k' = j
⊢ first ≤ ↑k' ∧ ↑k' ≤ last