rw [← ENNReal.coe_inv hp', ← ENNReal.coe_inv hq'] at hpq
case inl.intro.some.some.inv_add_inv_conj
p q : ℝ≥0
hpq : (↑p)⁻¹ + (↑q)⁻¹ = 1
hp✝ : True
hp : 1 < p
hp' : ¬p = 0
hq✝ : True
hq : 1 < q
hq' : ¬q = 0
⊢ p⁻¹ + q⁻¹ = 1
case inl.intro.some.some.inv_add_inv_conj
p q : ℝ≥0
hpq : ↑p⁻¹ + ↑q⁻¹ = 1
hp✝ : True
hp : 1 < p
hp' : ¬p = 0
hq✝ : True
hq : 1 < q
hq' : ¬q = 0
⊢ p⁻¹ + q⁻¹ = 1