feat: characterize when T-division equals zero

[bollu]

This PR adds the lemma Int.tdiv_eq_zero_iff_natAbs_lt_or_eq_zero which shows that T-division equals zero iff the absolute value of the numerator is less than the denominator, or the denominator equals zero:

@[simp] theorem tdiv_eq_zero_iff_natAbs_lt_or_eq_zero {a : Int} {b : Int} :
    a.tdiv b = 0 ↔ (a.natAbs < b.natAbs ∨ b = 0):= by

This was used in reasoning about the MSB of BitVec.sdiv. The strategy was
superced, but this lemma was extracted from the earlier proof.

[bollu]

changelog-library

[ghost]

Mathlib CI status (docs):

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• ❗ Batteries/Mathlib CI will not be attempted unless your PR branches off the nightly-with-mathlib branch. Try git rebase ec9ff12fc65316c902224aa895a32ae943dcc762 --onto faffe863343211d03d07d4ef19d90a2aa9d6fc8c. You can force Mathlib CI using the force-mathlib-ci label. (2025-06-14 14:47:32)

[tobiasgrosser]

LGTM.

[tobiasgrosser]

LGTM. Thank you, @bollu.

[mathlib-lean-pr-testing]

Mathlib CI status (docs):

• ❗ Batteries/Mathlib CI will not be attempted unless your PR branches off the nightly-with-mathlib branch. Try git rebase 2a5b1a2f7ec519ab9f6196acd8c8e735c7e5a2b2 --onto ac0f56e6f6c8022a0b8df4ffd0738bc20723e1ef. You can force Mathlib CI using the force-mathlib-ci label. (2026-08-31 05:29:38)

[leanprover-bot]

Reference manual CI status:

• ❗ Reference manual CI will not be attempted unless your PR branches off the nightly-with-manual branch. Try git rebase 2a5b1a2f7ec519ab9f6196acd8c8e735c7e5a2b2 --onto e991a05e359a25988f49bff3ab8af986e959b866. You can force reference manual CI using the force-manual-ci label. (2026-08-31 05:29:39)