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feat(ForMathlib): effective lattice-point count terminal export (2/2) - #18

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feat(ForMathlib): effective lattice-point count terminal export (2/2)#18
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@CBirkbeck CBirkbeck commented Jun 18, 2026

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Part 2 of 2 of the effective lattice-point count (split from PR #11) — completes LatticePointCount.lean. Stacked on part 1; GitHub retargets the base to master as parents merge.

Adds:

  • exists_card_inter_smul_lattice_sub_volume_mul_pow_le — the terminal export: #(s ∩ t⁻¹·ℤ^ι) = vol(s)·tᵈ + O(tᵈ⁻¹), the effective (explicit-rate) form of mathlib's rate-free tendsto_card_div_pow_atTop_volume.

Assembles the per-scale bridge abs_card_inter_sub_volume_mul_pow_le (part 1) with the O(nᵈ⁻¹) boundary-cell bound ncard_index_image_frontier_le (IndexImageCount stack, part 4/4).

Builds green on the v4.31.0-rc1 / mathlib-master pin.

🤖 Generated with Claude Code


Final slice (stacked on 1/2) — completes `LatticePointCount.lean`. Adds:

* `exists_card_inter_smul_lattice_sub_volume_mul_pow_le` —
  `#(s ∩ t⁻¹·ℤ^ι) = vol(s)·tᵈ + O(tᵈ⁻¹)`, the effective form of mathlib's
  rate-free `tendsto_card_div_pow_atTop_volume`.

Assembles the per-scale bridge (1/2) with the `O(nᵈ⁻¹)` boundary-cell bound
(`ncard_index_image_frontier_le`, from the IndexImageCount stack).

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
CBirkbeck added a commit that referenced this pull request Jul 13, 2026
… code)

- trim module docstring to this slice: drop the exists_... terminal-export
  bullet (it lands in lpc-2 / #18) and reword the intro to the per-scale
  bridge; remaining refs (tendsto_card_div_pow_atTop_volume,
  abs_card_inter_sub_volume_mul_pow_le, ncard_index_image_frontier_le) all exist
- remove unneeded classical (by_cases is already classical in mathlib)
- remove unused hn0 positivity have
- drop unused set-equation names with hInside / hMeet / hBd; keep hTag, hV

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
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