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```python
# AI Dev Tool: FastAPI Lean Theorem Prover Micro-SaaS
# ================================================
# A production-ready, type-safe boilerplate for building
# reliable and scalable micro-SaaS applications with FastAPI and Pydantic.

from fastapi import FastAPI, HTTPException
from pydantic import BaseModel, Field
from typing import Optional
import logging

# Initialize the FastAPI application
app = FastAPI(title="FastAPI Lean Theorem Prover Micro-SaaS",
              description="A production-ready, type-safe boilerplate for building reliable and scalable micro-SaaS applications.",
              version="1.0.0")

# Define a type-safe model for the theorem prover input
class TheoremProverInput(BaseModel):
    """The input model for the theorem prover."""
    statement: str = Field(..., description="The statement to prove.")
    premises: Optional[list[str]] = Field(None, description="The premises to use for the proof.")

# Define a type-safe model for the theorem prover output
class TheoremProverOutput(BaseModel):
    """The output model for the theorem prover."""
    proof: str = Field(..., description="The proof of the statement.")
    status: str = Field(...

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