case h_bot

⊢ EReal.abs ⊥ = 0 ↔ ⊥ = 0

case h_real
a✝ : ℝ
⊢ EReal.abs ↑a✝ = 0 ↔ ↑a✝ = 0

case h_top

⊢ EReal.abs ⊤ = 0 ↔ ⊤ = 0
x : EReal
⊢ EReal.abs x = 0 ↔ x = 0
induction x using EReal.rec
no goals
case h_bot

⊢ EReal.abs ⊥ = 0 ↔ ⊥ = 0
simp only [abs_bot, ENNReal.top_ne_zero, bot_ne_zero]
no goals
case h_real
a✝ : ℝ
⊢ EReal.abs ↑a✝ = 0 ↔ ↑a✝ = 0
simp only [abs_def, coe_eq_zero, ENNReal.ofReal_eq_zero, abs_nonpos_iff]
no goals
case h_top

⊢ EReal.abs ⊤ = 0 ↔ ⊤ = 0
simp only [abs_top, ENNReal.top_ne_zero, top_ne_zero]