Simplify the strict-step extraction in LTSeries.exists_unzip

Derive c.head < c 1 from the series' StrictMono instance and Fin.one_pos'
instead of unfolding c.step with manual Fin.succ index arithmetic.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

lean/Spa/Lattice/Prod.lean

@@ -27,16 +27,13 @@ theorem LTSeries.exists_unzip (c : LTSeries (α × β)) :
   | succ n ih =>
     intro c hn
     have h0 : c.length ≠ 0 := by omega
+    haveI : NeZero c.length := ⟨h0⟩
     obtain ⟨c₁, c₂, hh₁, hl₁, hh₂, hl₂, hlen⟩ :=
       ih (c.tail h0) (by simp [RelSeries.tail_length, hn])
     rw [RelSeries.last_tail] at hl₁ hl₂
     rw [RelSeries.head_tail] at hh₁ hh₂
     rw [RelSeries.tail_length] at hlen
-    have hstep : c.head < c 1 := by
-      have h := c.step ⟨0, by omega⟩
-      have h1 : (⟨0, by omega⟩ : Fin c.length).succ = 1 := by
-        ext; simp [Fin.val_one, Nat.mod_eq_of_lt (by omega : 1 < c.length + 1)]
-      rwa [h1] at h
+    have hstep : c.head < c 1 := c.strictMono Fin.one_pos'
     obtain ⟨hle1, hle2⟩ := Prod.le_def.mp hstep.le
     rcases eq_or_lt_of_le hle1 with heq1 | hlt1 <;>
       rcases eq_or_lt_of_le hle2 with heq2 | hlt2