"""Executable examples for Chapters 30 and 32: delete a hypothesis, ask Z3.

For a claim "H1 and ... and Hn imply G", dropping Hi and asking Z3 for a model of
(the other hypotheses and not G):
  sat   -> Hi is load-bearing; the model shows why
  unsat -> Hi is redundant given the others (or the claim is vacuous without it)

Run from the repository root:

    uv run python content/examples/math/part4/part4_assumption_deletion_demo.py

ILLUSTRATIVE. Not versioned claims; no EvidenceResult. A Z3 `sat` is a candidate
witness that should be substituted back before it is called a refutation
(Chapter 5), and `unsat` holds only for the encoding below (Chapter 10).
Square root is encoded as a relation (s > 0, s*s = 1 - v*v), NOT Lean's junk-value
convention, so results on that encoding can differ from Lean's (Chapter 11).
"""

import z3

t, x, v, g = z3.Reals("t x v gamma")
s = z3.Real("s")  # sqrt(1 - v^2) as a relation


def check(label, hyps, goal):
    solver = z3.Solver()
    solver.add(*hyps)
    solver.add(z3.Not(goal))
    r = solver.check()
    extra = ""
    if r == z3.sat:
        m = solver.model()
        extra = "  model: " + ", ".join(f"{d}={m[d]}" for d in m)
    print(f"{label:58s} {r!s:6s}{extra}")


gamma_rel = g * g * (1 - v * v) == 1
alg_goal = (g * (t - v * x)) ** 2 - (g * (x - v * t)) ** 2 == t * t - x * x

print("== Chapter 30: algebraic Lorentz claim")
check("full claim (gamma relation)", [gamma_rel], alg_goal)
check("drop gamma relation", [], alg_goal)
check("is |v|<1 redundant given the gamma relation?", [gamma_rel],
      z3.And(v > -1, v < 1))
check("does the gamma relation force gamma > 0?", [gamma_rel], g > 0)

print("\n== Chapter 30: Pythagorean coordinate claim")
ax, ay, bx, by, cx, cy = z3.Reals("ax ay bx by cx cy")
dot = (bx - ax) * (cx - ax) + (by - ay) * (cy - ay)
ab2 = (bx - ax) ** 2 + (by - ay) ** 2
ac2 = (cx - ax) ** 2 + (cy - ay) ** 2
bc2 = (cx - bx) ** 2 + (cy - by) ** 2
check("full claim (orthogonality)", [dot == 0], bc2 == ab2 + ac2)
check("drop orthogonality", [], bc2 == ab2 + ac2)

print("\n== Chapter 30: timelike order (gamma form)")
goal = g * (t - v * x) > 0
base = {"gamma>0": g > 0, "gamma relation": gamma_rel, "t>0": t > 0,
        "timelike t^2>x^2": t * t - x * x > 0}
check("full claim", list(base.values()), goal)
for name in base:
    check(f"drop {name}", [h for k, h in base.items() if k != name], goal)

print("\n== Chapter 32: physical hypotheses versus the algebraic hypothesis")
phys = [v > -1, v < 1, s > 0, s * s == 1 - v * v, g * s == 1]   # gamma = 1/sqrt(1-v^2)
check("physical hypotheses imply the gamma relation", phys, gamma_rel)
check("gamma relation implies physical gamma (gamma = 1/s)?",
      [gamma_rel, s > 0, s * s == 1 - v * v], g * s == 1)