awhecmu/canonical-drafter-extract-mathlib huggingface dataset:
-- Lean 4 proof step from Mathlib.Data.EReal.Operations (goal)
Goal:
a b : EReal
h : a < 0
h' : 0 < b
inl : (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₁ : (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0 → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₂ : 0 < a → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₃ : b < 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₄ : a = 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₅ : b = 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₆ : 0 < a → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₇ : b < 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₈ : a = 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₉ : b = 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₁₀ : 0 < a → ¬(0 < a ∨ 0 = a) → b < 0 ∨ b = 0
inl₁₁ : b < 0 → ¬(0 < a ∨ 0 = a) → b < 0 ∨ b = 0
inl₁₂ : a = 0 → ¬(0 < a ∨ 0 = a) → b < 0 ∨ b = 0
inl₁₃ : b = 0 → ¬(0 < a ∨ 0 = a) → b < 0 ∨ b = 0
inl₁₄ : 0 < a → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
⊢ (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0 ↔ (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
have inl₁₅ : 0 = a → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
Tactic: tauto
-- Lean 4 proof step from Mathlib.Data.EReal.Operations (goal)
Goal:
a b : EReal
h : a < 0
h' : 0 < b
inl : (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₁ : (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0 → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₂ : 0 < a → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₃ : b < 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₄ : a = 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₅ : b = 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₆ : 0 < a → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₇ : b < 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₈ : a = 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₉ : b = 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₁₀ : 0 < a → ¬(0 < a ∨ 0 = a) → b < 0 ∨ b = 0
inl₁₁ : b < 0 → ¬(0 < a ∨ 0 = a) → b < 0 ∨ b = 0
inl₁₂ : a = 0 → ¬(0 < a ∨ 0 = a) → b < 0 ∨ b = 0
inl₁₃ : b = 0 → ¬(0 < a ∨ 0 = a) → b < 0 ∨ b = 0
inl₁₄ : 0 < a → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₁₅ : 0 = a → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
⊢ (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0 ↔ (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
have inl₁₆ : b < 0 → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
Tactic: tauto
-- Lean 4 proof step from Mathlib.Data.EReal.Operations (goal)
Goal:
a b : EReal
h : a < 0
h' : 0 < b
inl : (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₁ : (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0 → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₂ : 0 < a → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₃ : b < 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₄ : a = 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₅ : b = 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₆ : 0 < a → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₇ : b < 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₈ : a = 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₉ : b = 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₁₀ : 0 < a → ¬(0 < a ∨ 0 = a) → b < 0 ∨ b = 0
inl₁₁ : b < 0 → ¬(0 < a ∨ 0 = a) → b < 0 ∨ b = 0
inl₁₂ : a = 0 → ¬(0 < a ∨ 0 = a) → b < 0 ∨ b = 0
inl₁₃ : b = 0 → ¬(0 < a ∨ 0 = a) → b < 0 ∨ b = 0
inl₁₄ : 0 < a → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₁₅ : 0 = a → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₁₆ : b < 0 → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
⊢ (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0 ↔ (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
have inl₁₇ : b = 0 → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
Tactic: tauto
-- Lean 4 proof step from Mathlib.Data.EReal.Operations (goal)
Goal:
a b : EReal
h : a < 0
h' : 0 < b
inl : (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₁ : (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0 → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₂ : 0 < a → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₃ : b < 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₄ : a = 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₅ : b = 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₆ : 0 < a → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₇ : b < 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₈ : a = 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₉ : b = 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₁₀ : 0 < a → ¬(0 < a ∨ 0 = a) → b < 0 ∨ b = 0
inl₁₁ : b < 0 → ¬(0 < a ∨ 0 = a) → b < 0 ∨ b = 0
inl₁₂ : a = 0 → ¬(0 < a ∨ 0 = a) → b < 0 ∨ b = 0
inl₁₃ : b = 0 → ¬(0 < a ∨ 0 = a) → b < 0 ∨ b = 0
inl₁₄ : 0 < a → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₁₅ : 0 = a → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₁₆ : b < 0 → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₁₇ : b = 0 → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₁₈ : 0 < a → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₁₉ : 0 = a → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₂₀ : b < 0 → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₂₁ : b = 0 → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
⊢ (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0 ↔ (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
have inl₂₂ : 0 < a → ¬(0 < a ∨ b < 0) → a = 0 ∨ b = 0
Tactic: tauto
-- Lean 4 proof step from Mathlib.Data.EReal.Operations (goal)
Goal:
a b : EReal
h : a < 0
h' : 0 < b
inl : (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₁ : (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0 → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₂ : 0 < a → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₃ : b < 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₄ : a = 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₅ : b = 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₆ : 0 < a → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₇ : b < 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₈ : a = 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₉ : b = 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₁₀ : 0 < a → ¬(0 < a ∨ 0 = a) → b < 0 ∨ b = 0
inl₁₁ : b < 0 → ¬(0 < a ∨ 0 = a) → b < 0 ∨ b = 0
inl₁₂ : a = 0 → ¬(0 < a ∨ 0 = a) → b < 0 ∨ b = 0
inl₁₃ : b = 0 → ¬(0 < a ∨ 0 = a) → b < 0 ∨ b = 0
inl₁₄ : 0 < a → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₁₅ : 0 = a → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₁₆ : b < 0 → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₁₇ : b = 0 → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₁₈ : 0 < a → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₁₉ : 0 = a → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₂₀ : b < 0 → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₂₁ : b = 0 → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₂₂ : 0 < a → ¬(0 < a ∨ b < 0) → a = 0 ∨ b = 0
⊢ (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0 ↔ (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
have inl₂₃ : 0 = a → ¬(0 < a ∨ b < 0) → a = 0 ∨ b = 0
Tactic: tauto
-- Lean 4 proof step from Mathlib.Data.EReal.Operations (goal)
Goal:
a b : EReal
h : a < 0
h' : 0 < b
inl : (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₁ : (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0 → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₂ : 0 < a → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₃ : b < 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₄ : a = 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₅ : b = 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₆ : 0 < a → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₇ : b < 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₈ : a = 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₉ : b = 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₁₀ : 0 < a → ¬(0 < a ∨ 0 = a) → b < 0 ∨ b = 0
inl₁₁ : b < 0 → ¬(0 < a ∨ 0 = a) → b < 0 ∨ b = 0
inl₁₂ : a = 0 → ¬(0 < a ∨ 0 = a) → b < 0 ∨ b = 0
inl₁₃ : b = 0 → ¬(0 < a ∨ 0 = a) → b < 0 ∨ b = 0
inl₁₄ : 0 < a → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₁₅ : 0 = a → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₁₆ : b < 0 → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₁₇ : b = 0 → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₁₈ : 0 < a → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₁₉ : 0 = a → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₂₀ : b < 0 → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₂₁ : b = 0 → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₂₂ : 0 < a → ¬(0 < a ∨ b < 0) → a = 0 ∨ b = 0
inl₂₃ : 0 = a → ¬(0 < a ∨ b < 0) → a = 0 ∨ b = 0
⊢ (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0 ↔ (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
have inl₂₄ : b < 0 → ¬(0 < a ∨ b < 0) → a = 0 ∨ b = 0
Tactic: tauto
-- Lean 4 proof step from Mathlib.Data.EReal.Operations (goal)
Goal:
a b : EReal
h : a < 0
h' : 0 < b
inl : (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₁ : (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0 → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₂ : 0 < a → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₃ : b < 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₄ : a = 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₅ : b = 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₆ : 0 < a → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₇ : b < 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₈ : a = 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₉ : b = 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₁₀ : 0 < a → ¬(0 < a ∨ 0 = a) → b < 0 ∨ b = 0
inl₁₁ : b < 0 → ¬(0 < a ∨ 0 = a) → b < 0 ∨ b = 0
inl₁₂ : a = 0 → ¬(0 < a ∨ 0 = a) → b < 0 ∨ b = 0
inl₁₃ : b = 0 → ¬(0 < a ∨ 0 = a) → b < 0 ∨ b = 0
inl₁₄ : 0 < a → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₁₅ : 0 = a → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₁₆ : b < 0 → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₁₇ : b = 0 → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₁₈ : 0 < a → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₁₉ : 0 = a → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₂₀ : b < 0 → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₂₁ : b = 0 → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₂₂ : 0 < a → ¬(0 < a ∨ b < 0) → a = 0 ∨ b = 0
inl₂₃ : 0 = a → ¬(0 < a ∨ b < 0) → a = 0 ∨ b = 0
inl₂₄ : b < 0 → ¬(0 < a ∨ b < 0) → a = 0 ∨ b = 0
⊢ (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0 ↔ (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
have inl₂₅ : b = 0 → ¬(0 < a ∨ b < 0) → a = 0 ∨ b = 0
Tactic: tauto
-- Lean 4 proof step from Mathlib.Data.EReal.Operations (goal)
Goal:
a b : EReal
h : a < 0
h' : 0 < b
inl : (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₁ : (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0 → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₂ : 0 < a → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₃ : b < 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₄ : a = 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₅ : b = 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₆ : 0 < a → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₇ : b < 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₈ : a = 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₉ : b = 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₁₀ : 0 < a → ¬(0 < a ∨ 0 = a) → b < 0 ∨ b = 0
inl₁₁ : b < 0 → ¬(0 < a ∨ 0 = a) → b < 0 ∨ b = 0
inl₁₂ : a = 0 → ¬(0 < a ∨ 0 = a) → b < 0 ∨ b = 0
inl₁₃ : b = 0 → ¬(0 < a ∨ 0 = a) → b < 0 ∨ b = 0
inl₁₄ : 0 < a → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₁₅ : 0 = a → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₁₆ : b < 0 → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₁₇ : b = 0 → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₁₈ : 0 < a → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₁₉ : 0 = a → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₂₀ : b < 0 → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₂₁ : b = 0 → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₂₂ : 0 < a → ¬(0 < a ∨ b < 0) → a = 0 ∨ b = 0
inl₂₃ : 0 = a → ¬(0 < a ∨ b < 0) → a = 0 ∨ b = 0
inl₂₄ : b < 0 → ¬(0 < a ∨ b < 0) → a = 0 ∨ b = 0
inl₂₅ : b = 0 → ¬(0 < a ∨ b < 0) → a = 0 ∨ b = 0
⊢ (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0 ↔ (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
have inl₂₆ : 0 < a → ¬0 < a → ¬0 = a → b < 0 ∨ b = 0
Tactic: tauto
-- Lean 4 proof step from Mathlib.Data.EReal.Operations (goal)
Goal:
a b : EReal
h : a < 0
h' : 0 < b
inl : (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₁ : (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0 → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₂ : 0 < a → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₃ : b < 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₄ : a = 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₅ : b = 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₆ : 0 < a → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₇ : b < 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₈ : a = 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₉ : b = 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₁₀ : 0 < a → ¬(0 < a ∨ 0 = a) → b < 0 ∨ b = 0
inl₁₁ : b < 0 → ¬(0 < a ∨ 0 = a) → b < 0 ∨ b = 0
inl₁₂ : a = 0 → ¬(0 < a ∨ 0 = a) → b < 0 ∨ b = 0
inl₁₃ : b = 0 → ¬(0 < a ∨ 0 = a) → b < 0 ∨ b = 0
inl₁₄ : 0 < a → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₁₅ : 0 = a → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₁₆ : b < 0 → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₁₇ : b = 0 → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₁₈ : 0 < a → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₁₉ : 0 = a → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₂₀ : b < 0 → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₂₁ : b = 0 → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₂₂ : 0 < a → ¬(0 < a ∨ b < 0) → a = 0 ∨ b = 0
inl₂₃ : 0 = a → ¬(0 < a ∨ b < 0) → a = 0 ∨ b = 0
inl₂₄ : b < 0 → ¬(0 < a ∨ b < 0) → a = 0 ∨ b = 0
inl₂₅ : b = 0 → ¬(0 < a ∨ b < 0) → a = 0 ∨ b = 0
inl₂₆ : 0 < a → ¬0 < a → ¬0 = a → b < 0 ∨ b = 0
⊢ (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0 ↔ (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
have inl₂₇ : b < 0 → ¬0 < a → ¬0 = a → b < 0 ∨ b = 0
Tactic: tauto
-- Lean 4 proof step from Mathlib.Data.EReal.Operations (goal)
Goal:
a b : EReal
h : a < 0
h' : 0 < b
inl : (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₁ : (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0 → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₂ : 0 < a → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₃ : b < 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₄ : a = 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₅ : b = 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₆ : 0 < a → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₇ : b < 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₈ : a = 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₉ : b = 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₁₀ : 0 < a → ¬(0 < a ∨ 0 = a) → b < 0 ∨ b = 0
inl₁₁ : b < 0 → ¬(0 < a ∨ 0 = a) → b < 0 ∨ b = 0
inl₁₂ : a = 0 → ¬(0 < a ∨ 0 = a) → b < 0 ∨ b = 0
inl₁₃ : b = 0 → ¬(0 < a ∨ 0 = a) → b < 0 ∨ b = 0
inl₁₄ : 0 < a → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₁₅ : 0 = a → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₁₆ : b < 0 → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₁₇ : b = 0 → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₁₈ : 0 < a → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₁₉ : 0 = a → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₂₀ : b < 0 → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₂₁ : b = 0 → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₂₂ : 0 < a → ¬(0 < a ∨ b < 0) → a = 0 ∨ b = 0
inl₂₃ : 0 = a → ¬(0 < a ∨ b < 0) → a = 0 ∨ b = 0
inl₂₄ : b < 0 → ¬(0 < a ∨ b < 0) → a = 0 ∨ b = 0
inl₂₅ : b = 0 → ¬(0 < a ∨ b < 0) → a = 0 ∨ b = 0
inl₂₆ : 0 < a → ¬0 < a → ¬0 = a → b < 0 ∨ b = 0
inl₂₇ inl₂₈ : b < 0 → ¬0 < a → ¬0 = a → b < 0 ∨ b = 0
⊢ (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0 ↔ (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
have inl₂₉ : b < 0 → ¬0 < a → ¬0 = a → ¬b < 0 → b = 0
Tactic: tauto
-- Lean 4 proof step from Mathlib.Data.EReal.Operations (goal)
Goal:
a b : EReal
h : a < 0
h' : 0 < b
inl : (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₁ : (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0 → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₂ : 0 < a → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₃ : b < 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₄ : a = 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₅ : b = 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₆ : 0 < a → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₇ : b < 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₈ : a = 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₉ : b = 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₁₀ : 0 < a → ¬(0 < a ∨ 0 = a) → b < 0 ∨ b = 0
inl₁₁ : b < 0 → ¬(0 < a ∨ 0 = a) → b < 0 ∨ b = 0
inl₁₂ : a = 0 → ¬(0 < a ∨ 0 = a) → b < 0 ∨ b = 0
inl₁₃ : b = 0 → ¬(0 < a ∨ 0 = a) → b < 0 ∨ b = 0
inl₁₄ : 0 < a → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₁₅ : 0 = a → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₁₆ : b < 0 → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₁₇ : b = 0 → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₁₈ : 0 < a → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₁₉ : 0 = a → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₂₀ : b < 0 → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₂₁ : b = 0 → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₂₂ : 0 < a → ¬(0 < a ∨ b < 0) → a = 0 ∨ b = 0
inl₂₃ : 0 = a → ¬(0 < a ∨ b < 0) → a = 0 ∨ b = 0
inl₂₄ : b < 0 → ¬(0 < a ∨ b < 0) → a = 0 ∨ b = 0
inl₂₅ : b = 0 → ¬(0 < a ∨ b < 0) → a = 0 ∨ b = 0
inl₂₆ : 0 < a → ¬0 < a → ¬0 = a → b < 0 ∨ b = 0
inl₂₇ inl₂₈ : b < 0 → ¬0 < a → ¬0 = a → b < 0 ∨ b = 0
inl₂₉ : b < 0 → ¬0 < a → ¬0 = a → ¬b < 0 → b = 0
⊢ (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0 ↔ (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
have inl₃₀ : a = 0 → ¬0 < a → ¬0 = a → b < 0 ∨ b = 0
Tactic: tauto
-- Lean 4 proof step from Mathlib.Data.EReal.Operations (goal)
Goal:
a b : EReal
h : a < 0
h' : 0 < b
inl : (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₁ : (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0 → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₂ : 0 < a → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₃ : b < 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₄ : a = 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₅ : b = 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₆ : 0 < a → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₇ : b < 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₈ : a = 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₉ : b = 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₁₀ : 0 < a → ¬(0 < a ∨ 0 = a) → b < 0 ∨ b = 0
inl₁₁ : b < 0 → ¬(0 < a ∨ 0 = a) → b < 0 ∨ b = 0
inl₁₂ : a = 0 → ¬(0 < a ∨ 0 = a) → b < 0 ∨ b = 0
inl₁₃ : b = 0 → ¬(0 < a ∨ 0 = a) → b < 0 ∨ b = 0
inl₁₄ : 0 < a → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₁₅ : 0 = a → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₁₆ : b < 0 → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₁₇ : b = 0 → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₁₈ : 0 < a → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₁₉ : 0 = a → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₂₀ : b < 0 → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₂₁ : b = 0 → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₂₂ : 0 < a → ¬(0 < a ∨ b < 0) → a = 0 ∨ b = 0
inl₂₃ : 0 = a → ¬(0 < a ∨ b < 0) → a = 0 ∨ b = 0
inl₂₄ : b < 0 → ¬(0 < a ∨ b < 0) → a = 0 ∨ b = 0
inl₂₅ : b = 0 → ¬(0 < a ∨ b < 0) → a = 0 ∨ b = 0
inl₂₆ : 0 < a → ¬0 < a → ¬0 = a → b < 0 ∨ b = 0
inl₂₇ inl₂₈ : b < 0 → ¬0 < a → ¬0 = a → b < 0 ∨ b = 0
inl₂₉ : b < 0 → ¬0 < a → ¬0 = a → ¬b < 0 → b = 0
inl₃₀ inl₃₁ : a = 0 → ¬0 < a → ¬0 = a → b < 0 ∨ b = 0
⊢ (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0 ↔ (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
have inl₃₂ : a = 0 → ¬0 < a → ¬0 = a → ¬b < 0 → b = 0
Tactic: tauto
-- Lean 4 proof step from Mathlib.Data.EReal.Operations (goal)
Goal:
a b : EReal
h : a < 0
h' : 0 < b
inl : (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₁ : (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0 → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₂ : 0 < a → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₃ : b < 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₄ : a = 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₅ : b = 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₆ : 0 < a → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₇ : b < 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₈ : a = 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₉ : b = 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₁₀ : 0 < a → ¬(0 < a ∨ 0 = a) → b < 0 ∨ b = 0
inl₁₁ : b < 0 → ¬(0 < a ∨ 0 = a) → b < 0 ∨ b = 0
inl₁₂ : a = 0 → ¬(0 < a ∨ 0 = a) → b < 0 ∨ b = 0
inl₁₃ : b = 0 → ¬(0 < a ∨ 0 = a) → b < 0 ∨ b = 0
inl₁₄ : 0 < a → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₁₅ : 0 = a → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₁₆ : b < 0 → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₁₇ : b = 0 → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₁₈ : 0 < a → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₁₉ : 0 = a → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₂₀ : b < 0 → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₂₁ : b = 0 → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₂₂ : 0 < a → ¬(0 < a ∨ b < 0) → a = 0 ∨ b = 0
inl₂₃ : 0 = a → ¬(0 < a ∨ b < 0) → a = 0 ∨ b = 0
inl₂₄ : b < 0 → ¬(0 < a ∨ b < 0) → a = 0 ∨ b = 0
inl₂₅ : b = 0 → ¬(0 < a ∨ b < 0) → a = 0 ∨ b = 0
inl₂₆ : 0 < a → ¬0 < a → ¬0 = a → b < 0 ∨ b = 0
inl₂₇ inl₂₈ : b < 0 → ¬0 < a → ¬0 = a → b < 0 ∨ b = 0
inl₂₉ : b < 0 → ¬0 < a → ¬0 = a → ¬b < 0 → b = 0
inl₃₀ inl₃₁ : a = 0 → ¬0 < a → ¬0 = a → b < 0 ∨ b = 0
inl₃₂ : a = 0 → ¬0 < a → ¬0 = a → ¬b < 0 → b = 0
⊢ (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0 ↔ (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
have inl₃₃ : b = 0 → ¬0 < a → ¬0 = a → b < 0 ∨ b = 0
Tactic: tauto
-- Lean 4 proof step from Mathlib.Data.EReal.Operations (goal)
Goal:
a b : EReal
h : a < 0
h' : 0 < b
inl : (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₁ : (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0 → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₂ : 0 < a → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₃ : b < 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₄ : a = 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₅ : b = 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₆ : 0 < a → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₇ : b < 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₈ : a = 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₉ : b = 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₁₀ : 0 < a → ¬(0 < a ∨ 0 = a) → b < 0 ∨ b = 0
inl₁₁ : b < 0 → ¬(0 < a ∨ 0 = a) → b < 0 ∨ b = 0
inl₁₂ : a = 0 → ¬(0 < a ∨ 0 = a) → b < 0 ∨ b = 0
inl₁₃ : b = 0 → ¬(0 < a ∨ 0 = a) → b < 0 ∨ b = 0
inl₁₄ : 0 < a → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₁₅ : 0 = a → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₁₆ : b < 0 → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₁₇ : b = 0 → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₁₈ : 0 < a → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₁₉ : 0 = a → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₂₀ : b < 0 → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₂₁ : b = 0 → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₂₂ : 0 < a → ¬(0 < a ∨ b < 0) → a = 0 ∨ b = 0
inl₂₃ : 0 = a → ¬(0 < a ∨ b < 0) → a = 0 ∨ b = 0
inl₂₄ : b < 0 → ¬(0 < a ∨ b < 0) → a = 0 ∨ b = 0
inl₂₅ : b = 0 → ¬(0 < a ∨ b < 0) → a = 0 ∨ b = 0
inl₂₆ : 0 < a → ¬0 < a → ¬0 = a → b < 0 ∨ b = 0
inl₂₇ inl₂₈ : b < 0 → ¬0 < a → ¬0 = a → b < 0 ∨ b = 0
inl₂₉ : b < 0 → ¬0 < a → ¬0 = a → ¬b < 0 → b = 0
inl₃₀ inl₃₁ : a = 0 → ¬0 < a → ¬0 = a → b < 0 ∨ b = 0
inl₃₂ : a = 0 → ¬0 < a → ¬0 = a → ¬b < 0 → b = 0
inl₃₃ inl₃₄ : b = 0 → ¬0 < a → ¬0 = a → b < 0 ∨ b = 0
⊢ (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0 ↔ (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
have inl₃₅ : b = 0 → ¬0 < a → ¬0 = a → ¬b < 0 → b = 0
Tactic: tauto
-- Lean 4 proof step from Mathlib.Data.EReal.Operations (goal)
Goal:
a b : EReal
h : a < 0
h' : 0 < b
inl : (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₁ : (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0 → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₂ : 0 < a → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₃ : b < 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₄ : a = 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₅ : b = 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₆ : 0 < a → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₇ : b < 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₈ : a = 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₉ : b = 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₁₀ : 0 < a → ¬(0 < a ∨ 0 = a) → b < 0 ∨ b = 0
inl₁₁ : b < 0 → ¬(0 < a ∨ 0 = a) → b < 0 ∨ b = 0
inl₁₂ : a = 0 → ¬(0 < a ∨ 0 = a) → b < 0 ∨ b = 0
inl₁₃ : b = 0 → ¬(0 < a ∨ 0 = a) → b < 0 ∨ b = 0
inl₁₄ : 0 < a → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₁₅ : 0 = a → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₁₆ : b < 0 → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₁₇ : b = 0 → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₁₈ : 0 < a → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₁₉ : 0 = a → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₂₀ : b < 0 → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₂₁ : b = 0 → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₂₂ : 0 < a → ¬(0 < a ∨ b < 0) → a = 0 ∨ b = 0
inl₂₃ : 0 = a → ¬(0 < a ∨ b < 0) → a = 0 ∨ b = 0
inl₂₄ : b < 0 → ¬(0 < a ∨ b < 0) → a = 0 ∨ b = 0
inl₂₅ : b = 0 → ¬(0 < a ∨ b < 0) → a = 0 ∨ b = 0
inl₂₆ : 0 < a → ¬0 < a → ¬0 = a → b < 0 ∨ b = 0
inl₂₇ inl₂₈ : b < 0 → ¬0 < a → ¬0 = a → b < 0 ∨ b = 0
inl₂₉ : b < 0 → ¬0 < a → ¬0 = a → ¬b < 0 → b = 0
inl₃₀ inl₃₁ : a = 0 → ¬0 < a → ¬0 = a → b < 0 ∨ b = 0
inl₃₂ : a = 0 → ¬0 < a → ¬0 = a → ¬b < 0 → b = 0
inl₃₃ inl₃₄ : b = 0 → ¬0 < a → ¬0 = a → b < 0 ∨ b = 0
inl₃₅ : b = 0 → ¬0 < a → ¬0 = a → ¬b < 0 → b = 0
⊢ (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0 ↔ (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
have inl₃₆ : 0 < a → ¬0 < a → ¬b < 0 → a = 0 ∨ b = 0
Tactic: tauto
-- Lean 4 proof step from Mathlib.Data.EReal.Operations (goal)
Goal:
a b : EReal
h : a < 0
h' : 0 < b
inl : (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₁ : (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0 → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₂ : 0 < a → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₃ : b < 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₄ : a = 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₅ : b = 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₆ : 0 < a → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₇ : b < 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₈ : a = 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₉ : b = 0 → (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
inl₁₀ : 0 < a → ¬(0 < a ∨ 0 = a) → b < 0 ∨ b = 0
inl₁₁ : b < 0 → ¬(0 < a ∨ 0 = a) → b < 0 ∨ b = 0
inl₁₂ : a = 0 → ¬(0 < a ∨ 0 = a) → b < 0 ∨ b = 0
inl₁₃ : b = 0 → ¬(0 < a ∨ 0 = a) → b < 0 ∨ b = 0
inl₁₄ : 0 < a → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₁₅ : 0 = a → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₁₆ : b < 0 → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₁₇ : b = 0 → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₁₈ : 0 < a → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₁₉ : 0 = a → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₂₀ : b < 0 → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₂₁ : b = 0 → (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0
inl₂₂ : 0 < a → ¬(0 < a ∨ b < 0) → a = 0 ∨ b = 0
inl₂₃ : 0 = a → ¬(0 < a ∨ b < 0) → a = 0 ∨ b = 0
inl₂₄ : b < 0 → ¬(0 < a ∨ b < 0) → a = 0 ∨ b = 0
inl₂₅ : b = 0 → ¬(0 < a ∨ b < 0) → a = 0 ∨ b = 0
inl₂₆ : 0 < a → ¬0 < a → ¬0 = a → b < 0 ∨ b = 0
inl₂₇ inl₂₈ : b < 0 → ¬0 < a → ¬0 = a → b < 0 ∨ b = 0
inl₂₉ : b < 0 → ¬0 < a → ¬0 = a → ¬b < 0 → b = 0
inl₃₀ inl₃₁ : a = 0 → ¬0 < a → ¬0 = a → b < 0 ∨ b = 0
inl₃₂ : a = 0 → ¬0 < a → ¬0 = a → ¬b < 0 → b = 0
inl₃₃ inl₃₄ : b = 0 → ¬0 < a → ¬0 = a → b < 0 ∨ b = 0
inl₃₅ : b = 0 → ¬0 < a → ¬0 = a → ¬b < 0 → b = 0
inl₃₆ : 0 < a → ¬0 < a → ¬b < 0 → a = 0 ∨ b = 0
⊢ (0 < a ∨ b < 0) ∨ a = 0 ∨ b = 0 ↔ (0 < a ∨ 0 = a) ∨ b < 0 ∨ b = 0
have inl₃₇ : 0 = a → ¬0 < a → ¬b < 0 → a = 0 ∨ b = 0
Tactic: tauto