Lean 4 fork for HoTT-compatible kernel extensions (Path types, transport, HITs). Maintained against upstream leanprover/lean4.
e7e57d40c4
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. |
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