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r-irber-irbe/proof-skills/skills/hol-metamath-adapter/SKILL.md

hol-metamath-adapter

Skill3 starsChanged 26 days agoApache-2.0View on GitHub

USE FOR: translating HOL Light (.ml tactical scripts) and Metamath (set.mm ZFC proofs) into Lean 4. DO NOT USE FOR: Rocq ports (@rocq-proof-adapter) or Isabelle ports (@isabelle-isar-adapter). TRIGGERS: HOL Light, Metamath, set.mm, MESON_TAC, REAL_ARITH_TAC, WORD_BLAST, uzind, 3eqtri.

The file

We split this skill into the rules it gives an agent

3 rules. About 0 are common, 0 are distinctive, and 3 are very specific to this project.

  • ≈0

    Common · estimate

    Many files like this have a rule of this kind.

  • ≈0

    Distinctive · estimate

    This author's own choices. Worth a look.

  • 3

    Very specific

    Tied to their project's names, files or tools. Probably skip.

  • Common
  • Distinctive
  • Very specific
  1. Very specific:

    Load Dialect & Concordance Map: Read references/dialects/hol_light.json or references/dialects/metamath.json and query lean_search(source: …

    line 40
  2. Very specific:

    STOP: when porting Metamath m - n where m, n e.

    line 52
  3. Very specific:

    STOP: when porting HOL Light has_integral on improper oscillating functions.

    line 56

≈ “Common” is an estimate: at least 1 in 5 of the 350,495 skill files we read have a rule of the same kind, not the same words. “Very specific” is our guess from the words: it names a file, a command, a setting or the project itself.

Keep what fits and drop the rest. Your version, ready for your agents.
Files
SKILL.md

HOL Light & Metamath (set.mm) Proof Adapter (hol_light / metamath -> lean4)

Translate HOL Light OCaml tactical scripts (THEN, THENL, MESON_TAC, REAL_ARITH_TAC, REAL_RING, WORD_BLAST, real^N analysis) and Metamath set.mm ZFC deduction trees (syl, mpd, 3eqtri, uzind, fsum, extensible slot structures) into structured Lean 4 + Mathlib4.

Routing

  • USE FOR: porting HOL Light .ml theorems (multivariate analysis, Flyspeck, s2n-bignum word proofs) and Metamath set.mm / iset.mm theorems into Lean 4.
  • DO NOT USE FOR: Rocq/MathComp .v ports (delegate to @rocq-proof-adapter); Isabelle/Isar .thy ports (delegate to @isabelle-isar-adapter).
  • TRIGGERS: HOL Light, Metamath, set.mm, MESON_TAC, REAL_ARITH_TAC, REAL_RING, WORD_BLAST, SUBGOAL_THEN, 3eqtri, uzind, fsum.

Workflow

  1. Load Dialect & Concordance Map: Read references/dialects/hol_light.json or references/dialects/metamath.json and query lean_search(source: "concordance") for CONC-01..20.
  2. Lift Untyped / Predicate Domains to Lean Types (CONC-04, CONC-14):
    • Metamath x e. N, y e. R, G e. Grp -> typed binders (x : Nat), (y : Real), {G : Type*} [Group G].
    • HOL Light s : A -> bool finite sums nsum (m..n) f -> ∑ i ∈ Finset.Icc m n, f i.
  3. Collapse Low-Level Plumbing Chains into High-Level Tactics (CONC-05, CONC-13, CONC-18):
    • Collapse 20-100 step Metamath syl/mpd/addass/leadd1i chains into tauto, ring, linarith, omega, or positivity.

Recovery & STOP

  • STOP when porting Metamath m - n where m, n e. N: in set.mm, N c_ Z c_ C so 2 - 5 = -3, whereas in Lean (2 - 5 : Nat) = 0! Either cast to Int via zify or prove n <= m before using Nat.sub.
  • STOP when porting HOL Light has_integral on improper oscillating functions; verify IntegrableOn f s volume for Mathlib Bochner integration.

Handoffs

  • Predecessors: skill:lean-gateway, skill:itp-cross-porting, skill:lean-specification.
  • Successors: skill:lean-proof, skill:lean-proof-review, skill:lean-axiom-closure.

Detailed reference

Full encyclopedic reference, decision trees, and lookup tables live in references/hol-metamath-adapter-handbook.md .

See also

  • ../../references/hol-metamath-adapter-handbook.md -- Complete hol-metamath-adapter Handbook
  • ../lean-gateway/SKILL.md -- Top-level skill router

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