conv at hinv => simp only [hik, if_neg]; change k.1 > i
case h
n i : Nat
h : i + 1 < n
k : Fin n
hlt : k < { val := i + 1, isLt := h }
hinv✝ : (transposAdj i h)[↑k] > (transposAdj i h)[↑{ val := i + 1, isLt := h }]
hinv :
  (if i = ↑k then { val := i + 1, isLt := h }
    else
      { val := ↑k,
        isLt :=
          (_ : (fun x i => i < n) (transpos { val := i, isLt := (_ : i < n) } { val := i + 1, isLt := h }) ↑k) }) >
    { val := i, isLt := (_ : i < n) }
hik : ¬i = ↑k
⊢ False
case h
n i : Nat
h : i + 1 < n
k : Fin n
hlt : k < { val := i + 1, isLt := h }
hinv✝ : (transposAdj i h)[↑k] > (transposAdj i h)[↑{ val := i + 1, isLt := h }]
hinv : ↑k > i
hik : ¬i = ↑k
⊢ False