English
IH4 expresses the recursive step for the 24-argument case of multiplication, ensuring expansions propagate through cut expansions.
Русский
IH4 задаёт рекурсивный шаг для случая умножения с 24 аргументами, обеспечивая распространение разрезов.
LaTeX
$$$IH4\\ x_1 x_2 y := \\text{(recursive expansion property for 24-ary case)}$$$
Lean4
theorem ih₁₂ (ih' : ∀ a, ArgsRel a (Args.P24 x₁ x₂ y) → P124 a) : IH24 x₁ x₂ y :=
by
rw [IH24]
refine fun z ↦ ⟨?_, ?_, ?_⟩ <;> refine fun h ↦ ih' (Args.P24 _ _ _) (TransGen.single ?_)
· exact (cutExpand_add_right { y }).2 (cutExpand_pair_left h)
· exact (cutExpand_add_left { x₁ }).2 (cutExpand_pair_left h)
· exact (cutExpand_add_left { x₁ }).2 (cutExpand_pair_right h)