{"textDocument": {"uri": "file://plainGoal.lean"}, "position": {"line": 0, "character": 20}} {"rendered": "```lean\nα : Sort ?u\n⊢ α → α\n```", "goals": ["α : Sort ?u\n⊢ α → α"]} {"textDocument": {"uri": "file://plainGoal.lean"}, "position": {"line": 0, "character": 21}} {"rendered": "```lean\nα : Sort ?u\n⊢ α → α\n```", "goals": ["α : Sort ?u\n⊢ α → α"]} {"textDocument": {"uri": "file://plainGoal.lean"}, "position": {"line": 3, "character": 2}} {"rendered": "```lean\nα : Sort ?u\n⊢ α → α\n```", "goals": ["α : Sort ?u\n⊢ α → α"]} {"textDocument": {"uri": "file://plainGoal.lean"}, "position": {"line": 3, "character": 3}} {"rendered": "```lean\nα : Sort ?u\na : α\n⊢ α\n```", "goals": ["α : Sort ?u\na : α\n⊢ α"]} {"textDocument": {"uri": "file://plainGoal.lean"}, "position": {"line": 7, "character": 3}} {"rendered": "```lean\nα : Sort ?u\na : α\n⊢ α\n```", "goals": ["α : Sort ?u\na : α\n⊢ α"]} {"textDocument": {"uri": "file://plainGoal.lean"}, "position": {"line": 10, "character": 20}} {"rendered": "```lean\nα : Sort ?u\n⊢ α → α\n```", "goals": ["α : Sort ?u\n⊢ α → α"]} {"textDocument": {"uri": "file://plainGoal.lean"}, "position": {"line": 15, "character": 9}} {"rendered": "```lean\ncase zero\n⊢ 0 + Nat.zero = Nat.zero\n```", "goals": ["case zero\n⊢ 0 + Nat.zero = Nat.zero"]} {"textDocument": {"uri": "file://plainGoal.lean"}, "position": {"line": 17, "character": 5}} {"rendered": "```lean\ncase succ\nn✝ : Nat\n: 0 + n✝ = n✝\n⊢ 0 + Nat.succ n✝ = Nat.succ n✝\n```", "goals": ["case succ\nn✝ : Nat\n: 0 + n✝ = n✝\n⊢ 0 + Nat.succ n✝ = Nat.succ n✝"]} {"textDocument": {"uri": "file://plainGoal.lean"}, "position": {"line": 21, "character": 9}} {"rendered": "```lean\nα : Sort ?u\na : α\n⊢ α\n```", "goals": ["α : Sort ?u\na : α\n⊢ α"]} {"textDocument": {"uri": "file://plainGoal.lean"}, "position": {"line": 21, "character": 10}} {"rendered": "```lean\nα : Sort ?u\na : α\n⊢ α\n```", "goals": ["α : Sort ?u\na : α\n⊢ α"]} {"textDocument": {"uri": "file://plainGoal.lean"}, "position": {"line": 21, "character": 11}} {"rendered": "```lean\nα : Sort ?u\na : α\n⊢ α\n```", "goals": ["α : Sort ?u\na : α\n⊢ α"]} {"textDocument": {"uri": "file://plainGoal.lean"}, "position": {"line": 27, "character": 3}} {"rendered": "```lean\nn m : Nat\nh1 : n = m\nh2 : m = 0\n⊢ 0 = n\n```", "goals": ["n m : Nat\nh1 : n = m\nh2 : m = 0\n⊢ 0 = n"]} {"textDocument": {"uri": "file://plainGoal.lean"}, "position": {"line": 27, "character": 9}} {"rendered": "```lean\nn m : Nat\nh1 : n = m\nh2 : m = 0\n⊢ 0 = m\n```", "goals": ["n m : Nat\nh1 : n = m\nh2 : m = 0\n⊢ 0 = m"]} {"textDocument": {"uri": "file://plainGoal.lean"}, "position": {"line": 27, "character": 13}} {"rendered": "no goals", "goals": []} {"textDocument": {"uri": "file://plainGoal.lean"}, "position": {"line": 34, "character": 3}} {"rendered": "```lean\ncase zero\n⊢ 0 + Nat.zero = Nat.zero\n```", "goals": ["case zero\n⊢ 0 + Nat.zero = Nat.zero"]} {"textDocument": {"uri": "file://plainGoal.lean"}, "position": {"line": 40, "character": 3}} {"rendered": "```lean\ncase zero\n⊢ 0 + Nat.zero = Nat.zero\n```\n---\n```lean\ncase succ\nn✝ : Nat\n: 0 + n✝ = n✝\n⊢ 0 + Nat.succ n✝ = Nat.succ n✝\n```", "goals": ["case zero\n⊢ 0 + Nat.zero = Nat.zero", "case succ\nn✝ : Nat\n: 0 + n✝ = n✝\n⊢ 0 + Nat.succ n✝ = Nat.succ n✝"]} {"textDocument": {"uri": "file://plainGoal.lean"}, "position": {"line": 44, "character": 3}} {"rendered": "```lean\ncase zero\n⊢ 0 + Nat.zero = Nat.zero\n```\n---\n```lean\ncase succ\nn✝ : Nat\n⊢ 0 + Nat.succ n✝ = Nat.succ n✝\n```", "goals": ["case zero\n⊢ 0 + Nat.zero = Nat.zero", "case succ\nn✝ : Nat\n⊢ 0 + Nat.succ n✝ = Nat.succ n✝"]} {"textDocument": {"uri": "file://plainGoal.lean"}, "position": {"line": 48, "character": 3}} {"rendered": "```lean\na b : Nat\n⊢ a = b\n```", "goals": ["a b : Nat\n⊢ a = b"]} {"textDocument": {"uri": "file://plainGoal.lean"}, "position": {"line": 51, "character": 20}} {"rendered": "```lean\nα : Sort ?u\n⊢ α → α\n```", "goals": ["α : Sort ?u\n⊢ α → α"]} {"textDocument": {"uri": "file://plainGoal.lean"}, "position": {"line": 55, "character": 3}} {"rendered": "```lean\nα : Sort ?u\np : α → Prop\na b : α\ninst✝ : DecidablePred p\nh : ∀ {p : α → Prop} [inst : DecidablePred p], p a → p b\n⊢ p a\n```", "goals": ["α : Sort ?u\np : α → Prop\na b : α\ninst✝ : DecidablePred p\nh : ∀ {p : α → Prop} [inst : DecidablePred p], p a → p b\n⊢ p a"]} {"textDocument": {"uri": "file://plainGoal.lean"}, "position": {"line": 61, "character": 3}} {"rendered": "```lean\ncase left\n⊢ True\n```", "goals": ["case left\n⊢ True"]} {"textDocument": {"uri": "file://plainGoal.lean"}, "position": {"line": 63, "character": 3}} {"rendered": "```lean\ncase right\n⊢ False\n```", "goals": ["case right\n⊢ False"]} {"textDocument": {"uri": "file://plainGoal.lean"}, "position": {"line": 68, "character": 3}} {"rendered": "```lean\ncase left\n⊢ True\n```", "goals": ["case left\n⊢ True"]} {"textDocument": {"uri": "file://plainGoal.lean"}, "position": {"line": 70, "character": 3}} {"rendered": "```lean\ncase right\n⊢ False\n```", "goals": ["case right\n⊢ False"]} {"textDocument": {"uri": "file://plainGoal.lean"}, "position": {"line": 78, "character": 29}} {"rendered": "```lean\nt a n✝ : Nat\n: t * (a + n✝) = t * a + t * n✝\n⊢ t * (a + n✝) + t = t * a + t * Nat.succ n✝\n```\n---\n```lean\nt a n✝ : Nat\n: t * (a + n✝) = t * a + t * n✝\n⊢ t * (a + n✝) + t = t * a + (t * n✝ + t)\n```\n---\n```lean\nt a n✝ : Nat\n: t * (a + n✝) = t * a + t * n✝\n⊢ t * (a + n✝) + t = t * a + (t * n✝ + t)\n```", "goals": ["t a n✝ : Nat\n: t * (a + n✝) = t * a + t * n✝\n⊢ t * (a + n✝) + t = t * a + t * Nat.succ n✝", "t a n✝ : Nat\n: t * (a + n✝) = t * a + t * n✝\n⊢ t * (a + n✝) + t = t * a + (t * n✝ + t)", "t a n✝ : Nat\n: t * (a + n✝) = t * a + t * n✝\n⊢ t * (a + n✝) + t = t * a + (t * n✝ + t)"]} {"textDocument": {"uri": "file://plainGoal.lean"}, "position": {"line": 82, "character": 53}} {"rendered": "```lean\ncase nil\nα : Type ?u\nbs cs : List α\n⊢ [] ++ bs ++ cs = [] ++ (bs ++ cs)\n```", "goals": ["case nil\nα : Type ?u\nbs cs : List α\n⊢ [] ++ bs ++ cs = [] ++ (bs ++ cs)"]} {"textDocument": {"uri": "file://plainGoal.lean"}, "position": {"line": 82, "character": 54}} {"rendered": "```lean\ncase nil\nα : Type ?u\nbs cs : List α\n⊢ [] ++ bs ++ cs = [] ++ (bs ++ cs)\n```", "goals": ["case nil\nα : Type ?u\nbs cs : List α\n⊢ [] ++ bs ++ cs = [] ++ (bs ++ cs)"]} {"textDocument": {"uri": "file://plainGoal.lean"}, "position": {"line": 86, "character": 38}} {"rendered": "no goals", "goals": []} {"textDocument": {"uri": "file://plainGoal.lean"}, "position": {"line": 89, "character": 39}} null {"textDocument": {"uri": "file://plainGoal.lean"}, "position": {"line": 93, "character": 16}} {"rendered": "```lean\ncase left\n⊢ True\n```\n---\n```lean\ncase right\n⊢ False\n```", "goals": ["case left\n⊢ True", "case right\n⊢ False"]} {"textDocument": {"uri": "file://plainGoal.lean"}, "position": {"line": 97, "character": 8}} {"rendered": "```lean\n| True = True\n```", "goals": ["| True = True"]} {"textDocument": {"uri": "file://plainGoal.lean"}, "position": {"line": 99, "character": 4}} {"rendered": "```lean\n| True = True\n```", "goals": ["| True = True"]} {"textDocument": {"uri": "file://plainGoal.lean"}, "position": {"line": 101, "character": 2}} {"rendered": "no goals", "goals": []} {"textDocument": {"uri": "file://plainGoal.lean"}, "position": {"line": 105, "character": 2}} {"rendered": "```lean\n⊢ False\n```", "goals": ["⊢ False"]}