apply ofLen_contains_extendLenOne_image
case succ
p✝ p : LoopProgram
x' : ℕ
⊢ loop { index := Nat.succ x' } p ∈ ofLen (len p + Nat.succ x' + 1)
case succ.h₁
p✝ p : LoopProgram
x' : ℕ
⊢ ?succ.p ∈ ofLen (len p + Nat.succ x')

case succ.h₂
p✝ p : LoopProgram
x' : ℕ
⊢ loop { index := Nat.succ x' } p ∈ extendLenOne ?succ.p

case succ.p
p✝ p : LoopProgram
x' : ℕ
⊢ LoopProgram