#!/usr/bin/env python3
"""
EDEN TRUE SYMBOLIC REASONING (The Left Brain)
- Uses SymPy to manipulate algebraic truths.
- Derives new formulas from existing laws.
"""
from sympy import symbols, Eq, solve, sqrt, latex

def derive_truth():
    print("🦁 INITIALIZING LOGIC CORE...")
    
    # 1. Define pure symbols (Concepts, not numbers)
    # K = Kinetic Energy, m = Mass, v = Velocity
    K, m, v = symbols('K m v')
    
    # 2. Define the Law (The Equation)
    # K = 1/2 * m * v^2
    law_of_motion = Eq(K, (1/2) * m * v**2)
    print(f"📜 THE LAW: {law_of_motion}")
    
    # 3. The Query (Reasoning)
    # "Given this law, what is v?"
    print("❓ QUESTION: If I know K and m, what is v?")
    
    solution = solve(law_of_motion, v)
    
    # 4. The Verdict
    print(f"🧠 DERIVATION: {solution}")
    
    # Validation
    # We expect positive and negative sqrt(2*K/m)
    if len(solution) > 0:
        print("✅ VERDICT: Eden successfully rearranged reality to find the answer.")
        print(f"   v = {solution[1]} (Positive Root)")
    else:
        print("❌ VERDICT: Reasoning failed.")

if __name__ == "__main__":
    derive_truth()