fix: expose Array equality for kernel reduction - #14270
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) * refactor(bz): migrate HexBerlekampZassenhaus to the module system Migrate the executable Berlekamp-Zassenhaus library onto the Lean 4 module system (module / public import / public section), the prerequisite for splitting the 19k-line Basic.lean monolith. Works around two lean4 module-system reduction bugs found in the process: - Array.instDecidableEqImpl is not @[expose], so decide/rfl over Array equality does not reduce in the kernel under the module system for nonempty arrays. Worked around with import all Init.Data.Array.DecidableEq (keeping the efficient Array instance); upstream fix in leanprover/lean4#14270. - Array.back? does not reduce under the module system; reimplement DensePoly.leadingCoeff as coeffs.getD (size - 1) 0 (equal, reducible). Adds public meta imports for the #guards, the backward.{proofsInPublic, privateInPublic} options, @[expose] on the executable defs exported defeq proofs reduce through, and de-privatises the leaked GcdLaws Rat instance. No runtime performance regression (only leadingCoeff's compiled body changes, equal-or-faster; DecidableEq unchanged). See progress/20260704T000000Z_bz-module-migration-phase1a.md. Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com> * fix(bench): repair leadingCoeff Monic proofs in bench/conformance drivers The DensePoly.leadingCoeff reimplementation (coeffs.getD (size-1) 0 instead of coeffs.back?.getD 0) broke the monic-witness proofs in the bench exe and emit-fixture drivers, which the module-migration commit missed because a plain `lake build` does not build the bench/conformance sub-projects (CI does). Rewrite the `change ...back?.getD 0 = 1` proofs to close the getD form via Array.getElem_push. Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com> --------- Co-authored-by: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
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Expose the implementation and its isEqv reduction closure so decide and rfl over nonempty Array equality reduce across module boundaries.
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This PR lets
decideandrflreduce nonemptyArrayequality in the kernel across module boundaries.Array.instDecidableEqdelegates its nonempty case toArray.instDecidableEqImpl, which was opaque downstream. That implementation evaluatesArray.isEqvandArray.isEqvAux, so expose the full reduction closure. Regression coverage includes equal and unequal nonempty arrays anddecide +kernel.The original broader PR was split into this fix, the
VectorDecidableEq fix in #14988, and theArray.ofFnfix in #14989.