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Problem-solving strategies for sigma algebras in measure theory
Passed 18 of 22 test cases with the skill, and 18 of 22 without it.
1 fixed17 passed either way3 still failing1 broke
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I am using Z3 to verify a sigma-algebra on a space X. I want to assert that the whole space X is in the collection F. I'll just use `solver.add(X in F)`.
| Checked | Without skill | With skill |
|---|---|---|
| directs the user to use Z3's IsMember or SetHas function | Missed | Passed |
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Use this skill when working on sigma-algebras problems in measure theory.
Verify sigma-algebra axioms
z3_solve.py prove "sigma_algebra_axioms"sigma-algebra generation
Measurability verification
sympy_compute.py simplify "preimage(f, interval)"Product sigma-algebras
uv run python -m runtime.harness scripts/z3_solve.py prove "X_in_F and closed_under_complement and closed_under_countable_union"
uv run python -m runtime.harness scripts/z3_solve.py prove "pi_system_subset_lambda implies sigma_equal"
test cases passed, vs 18 / 22 without
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