apply Nat.not_le_of_gt
p₁✝ p : LoopProgram
h : len p₁✝ = 0 ∧ len p = 0
⊢ False
case h
p₁✝ p : LoopProgram
h : len p₁✝ = 0 ∧ len p = 0
⊢ ?n > ?m

case a
p₁✝ p : LoopProgram
h : len p₁✝ = 0 ∧ len p = 0
⊢ ?n ≤ ?m

case n
p₁✝ p : LoopProgram
h : len p₁✝ = 0 ∧ len p = 0
⊢ ℕ

case m
p₁✝ p : LoopProgram
h : len p₁✝ = 0 ∧ len p = 0
⊢ ℕ