proof(lean4): complete preservation + determinism (Lean parity with Coq)

[hyperpolymath]

What

Completes the phronesis Lean 4 type-safety proof — clears the two TODO/sorry placeholders (preservation, determinism) and makes the file genuinely compile + verify.

The proofs (ported from the complete Coq ../coq/Phronesis.v)

• Eval — big-step evaluation relation ValEnv → PhrExpr → PhrValue → Prop (mirrors Coq ρ ⊢ e ⇓ v).
• preservation — a well-typed closed expression evaluates to a value of its type.
• determinism — evaluation is deterministic.

Made it actually build (it never had been)

The file imported Mathlib but shipped with no build setup and several core errors, so it had never been checked. Now self-contained on core Lean (proofs use only cases/induction/omega/simp/injection): dropped the unused Mathlib imports; made size/containsDangerous structurally terminate via mutual helpers; dropped the (unused, non-core-derivable) DecidableEq PhrType; fixed le_refl/size annotations. Added lakefile.lean + lean-toolchain (Lean v4.12.0, no deps).

Verification

• lake build → success (core Lean only; CI needs just the toolchain).
• #print axioms: determinism depends on NO axioms, preservation only on propext, progress/subtype_trans none — no sorryAx anywhere.

This brings Lean to parity with the Coq development for the core type-safety metatheory. (Remaining phronesis proof scope — consensus/ethics-specific soundness — is separate, per the discussion.)

🤖 Draft opened by Claude Code.

https://claude.ai/code/session_01DQACj3RFmAPZaBPgR9SAaS

---

Generated by Claude Code

[github-actions]

🔍 Hypatia Security Scan

Findings: 30 issues detected

Severity	Count
🔴 Critical	0
🟠 High	7
🟡 Medium	23

View findings

[
  {
    "reason": "Action trufflesecurity/trufflehog@main needs attention",
    "type": "unpinned_action",
    "file": "secret-scanner.yml",
    "action": "pin_sha",
    "rule_module": "workflow_audit",
    "severity": "high"
  },
  {
    "reason": "Issue in secret-scanner.yml",
    "type": "missing_timeout_minutes",
    "file": "secret-scanner.yml",
    "action": "flag",
    "rule_module": "workflow_audit",
    "severity": "medium"
  },
  {
    "reason": "Issue in scorecard-enforcer.yml",
    "type": "scorecard_publish_with_run_step",
    "file": "scorecard-enforcer.yml",
    "action": "split_scorecard_publish_job",
    "rule_module": "workflow_audit",
    "severity": "high"
  },
  {
    "reason": "binary_to_term without :safe option -- deserialization attack (1 occurrences, CWE-502)",
    "type": "elixir_send_unsanitised",
    "file": "/home/runner/work/phronesis/phronesis/lib/phronesis/compiler.ex",
    "action": "flag",
    "rule_module": "code_safety",
    "severity": "high"
  },
  {
    "reason": "Nominal-only SAST in phronesis: codeql.yml language matrix contains no language present in the repo and lacks `actions`, so CodeQL records zero results on every commit. Remediation: set the CodeQL matrix to `language: actions`.",
    "type": "StaticAnalysis",
    "file": "/home/runner/work/phronesis/phronesis",
    "action": "auto_fix",
    "rule_module": "scorecard",
    "severity": "medium",
    "remediation": "Add CodeQL or equivalent SAST workflow.",
    "scorecard_check": "SAST"
  },
  {
    "reason": "Repository has 3 non-main remote branch(es). Policy: single main branch only.",
    "type": "GS007",
    "file": ".",
    "action": "delete_remote_branches",
    "rule_module": "git_state",
    "severity": "medium"
  },
  {
    "reason": "Code scanning (Hypatia): hypatia/structural_drift/SD007 -- Hypatia structural_drift: SD007 -- 2 day(s) old",
    "type": "CSA001",
    "file": ".claude/CLAUDE.md",
    "action": "review",
    "rule_module": "code_scanning_alerts",
    "severity": "medium"
  },
  {
    "reason": "Code scanning (Hypatia): hypatia/structural_drift/SD007 -- Hypatia structural_drift: SD007 -- 2 day(s) old",
    "type": "CSA001",
    "file": ".claude/CLAUDE.md",
    "action": "review",
    "rule_module": "code_scanning_alerts",
    "severity": "medium"
  },
  {
    "reason": "Code scanning (Hypatia): hypatia/structural_drift/SD007 -- Hypatia structural_drift: SD007 -- 2 day(s) old",
    "type": "CSA001",
    "file": ".claude/CLAUDE.md",
    "action": "review",
    "rule_module": "code_scanning_alerts",
    "severity": "medium"
  },
  {
    "reason": "Code scanning (Hypatia): hypatia/structural_drift/SD007 -- Hypatia structural_drift: SD007 -- 2 day(s) old",
    "type": "CSA001",
    "file": ".claude/CLAUDE.md",
    "action": "review",
    "rule_module": "code_scanning_alerts",
    "severity": "medium"
  }
]

Powered by Hypatia Neurosymbolic CI/CD Intelligence