cases p with | none => contradiction | some p =>
cases q with | none => contradiction | some q =>
simp at *
constructor
. norm_cast
. rw [← ENNReal.coe_inv hp', ← ENNReal.coe_inv hq'] at hpq
  norm_cast at hpq
case inl.intro
p q : ℝ≥0∞
hpq : p⁻¹ + q⁻¹ = 1
hp✝ : p ≠ ⊤
hq✝ : q ≠ ⊤
hp : 1 < p ∧ p ≠ ⊤
hq : 1 < q ∧ q ≠ ⊤
hp' : p ≠ 0
hq' : q ≠ 0
⊢ Real.IsConjExponent ↑(ENNReal.toNNReal p) ↑(ENNReal.toNNReal q)
no goals