Lean定理证明语言服务器

{
    "servers": {
        "lean-lsp": {
            "type": "stdio",
            "command": "uvx",
            "args": [
                "lean-lsp-mcp"
            ]
        }
    }
}

{
    "servers": {
        "lean-lsp": {
            "type": "stdio",
            "command": "wsl.exe",
            "args": [
                "uvx",
                "lean-lsp-mcp"
            ]
        }
    }
}

{
    "mcpServers": {
        "lean-lsp": {
            "command": "uvx",
            "args": ["lean-lsp-mcp"]
        }
    }
}

# Local-scoped MCP server
claude mcp add lean-lsp uvx lean-lsp-mcp

# OR project-scoped MCP server
# (creates or updates a .mcp.json file in the current directory)
claude mcp add lean-lsp -s project uvx lean-lsp-mcp

l20c42-l20c46, severity: 1
simp made no progress

l21c11-l21c45, severity: 1
function expected at
  h_empty
term has type
  T ∩ compl T = ∅

...

Before:
S : Type u_1
inst✝¹ : Fintype S
inst✝ : Nonempty S
P : Finset (Set S)
hPP : ∀ T ∈ P, ∀ U ∈ P, T ∩ U ≠ ∅
hPS : ¬∃ T ∉ P, ∀ U ∈ P, T ∩ U ≠ ∅
compl : Set S → Set S := fun T ↦ univ \ T
hcompl : ∀ T ∈ P, compl T ∉ P
all_subsets : Finset (Set S) := Finset.univ
h_comp_in_P : ∀ T ∉ P, compl T ∈ P
h_partition : ∀ (T : Set S), T ∈ P ∨ compl T ∈ P
⊢ P.card = 2 ^ (Fintype.card S - 1)
After:
no goals

The `sorry` tactic is a temporary placeholder for an incomplete tactic proof,
closing the main goal using `exact sorry`.

This is intended for stubbing-out incomplete parts of a proof while still having a syntactically correct proof skeleton.
Lean will give a warning whenever a proof uses `sorry`, so you aren't likely to miss it,
but you can double check if a theorem depends on `sorry` by looking for `sorryAx` in the output
of the `#print axioms my_thm` command, the axiom used by the implementation of `sorry`.

l1c1-l1c6, severity: 3
38

  rw [Nat.pow_sub (Fintype.card_pos_of_nonempty S)]:
S : Type u_1
inst✝¹ : Fintype S
inst✝ : Nonempty S
P : Finset (Set S)
hPP : ∀ T ∈ P, ∀ U ∈ P, T ∩ U ≠ ∅
hPS : ¬∃ T ∉ P, ∀ U ∈ P, T ∩ U ≠ ∅
⊢ P.card = 2 ^ (Fintype.card S - 1)

l14c7-l14c51, severity: 1
unknown constant 'Nat.pow_sub'

  by_contra h_neq:
 S : Type u_1
inst✝¹ : Fintype S
inst✝ : Nonempty S
P : Finset (Set S)
hPP : ∀ T ∈ P, ∀ U ∈ P, T ∩ U ≠ ∅
hPS : ¬∃ T ∉ P, ∀ U ∈ P, T ∩ U ≠ ∅
h_neq : ¬P.card = 2 ^ (Fintype.card S - 1)
⊢ False

...

  {
    "module_name": "Mathlib.Logic.Function.Basic",
    "kind": "theorem",
    "name": "Function.Bijective.injective",
    "signature": " {f : α → β} (hf : Bijective f) : Injective f",
    "type": "∀ {α : Sort u_1} {β : Sort u_2} {f : α → β}, Function.Bijective f → Function.Injective f",
    "value": ":= hf.1",
    "informal_name": "Bijectivity Implies Injectivity",
    "informal_description": "For any function $f \\colon \\alpha \\to \\beta$, if $f$ is bijective, then $f$ is injective."
  },
  ...

  {'id': 25217,
  'primary_declaration': {'lean_name': 'Nat.add'},
  'source_file': 'Init/Prelude.lean',
  'range_start_line': 1705,
  'range_end_line': 1715,
  'display_statement_text': '。。。',
  'docstring': '...',
  'informal_description': '...'},
  ...

[
  {
    "type": " (x : ℝ) : ℝ",
    "name": "Real.sin",
    "module": "Mathlib.Data.Complex.Trigonometric"
  },
  ...
]

  [
    [
      "/-- If `y : L` is a root of `minpoly K x`, then `minpoly K y = minpoly K x`. -/\ntheorem eq_of_root {x y : L} (hx : IsAlgebraic K x)\n    (h_ev : Polynomial.aeval y (minpoly K x) = 0) : minpoly K y = minpoly K x :=\n  ((eq_iff_aeval_minpoly_eq_zero hx.isIntegral).mpr h_ev).symm",
      
      "Let $L/K$ be a field extension, and let $x, y \\in L$ be elements such that $y$ is a root of the minimal polynomial of $x$ over $K$. If $x$ is algebraic over $K$, then the minimal polynomial of $y$ over $K$ is equal to the minimal polynomial of $x$ over $K$, i.e., $\\text{minpoly}_K(y) = \\text{minpoly}_K(x)$. This means that if $y$ satisfies the polynomial equation defined by $x$, then $y$ shares the same minimal polynomial as $x$."
    ],
    ...
  ]

[
  {
    "name": "Nat.mul_zero",
    "formal_type": "∀ (n : Nat), n * 0 = 0",
    "module": "Init.Data.Nat.Basic"
  },
  ...
]

[
  "MulOpposite.unop_injective",
  "MulOpposite.op_injective",
  "WellFoundedLT.induction",
  ...
]

{
    "servers": {
        "lean-lsp": {
            "type": "stdio",
            "command": "uvx",
            "args": [
                "lean-lsp-mcp"
            ],
            "env": {
                "LEAN_PROJECT_PATH": "/path/to/your/lean/project",
                "LEAN_LOG_LEVEL": "NONE"
            }
        }
    }
}