lean4-htt/src/Init/Data/Nat/Bitwise
Tobias Grosser e7e57d40c4
feat: add BitVec.[toNat|toFin|toInt]_[sshiftRight|sshiftRight'] (#7104)
This PR adds `BitVec.[toNat|toFin|toInt]_[sshiftRight|sshiftRight']`
plus variants with `of_msb_*`. While at it, we also add
`toInt_zero_length` and `toInt_of_zero_length`. In support of our main
theorem we add `toInt_shiftRight_lt` and `le_toInt_shiftRight`, which
make the main theorem automatically derivable via omega.

We also add four shift lemmas for `Int`: `le_shiftRight_of_nonpos`,
`shiftRight_le_of_nonneg`, `le_shiftRight_of_nonneg`,
`shiftRight_le_of_nonpos`, as well as `emod_eq_add_self_emod`,
`ediv_nonpos_of_nonpos_of_neg `, and`bmod_eq_emod_of_lt `. For `Nat` we
add `shiftRight_le`.

Beyond the lemmas directly needed in the proof, we added a couple more
to ensure the API is complete.

We also fix the casing of `toFin_ushiftRight` and rename `lt_toInt` to
`two_mul_lt_toInt` to avoid `'`-ed lemmas.
2025-03-11 09:51:37 +00:00
..
Basic.lean feat: add BitVec.[toNat|toFin|toInt]_[sshiftRight|sshiftRight'] (#7104) 2025-03-11 09:51:37 +00:00
Lemmas.lean chore: cleanup duplicate theorems (#7113) 2025-02-18 01:46:12 +00:00