Lean 4 fork for HoTT-compatible kernel extensions (Path types, transport, HITs). Maintained against upstream leanprover/lean4.
bc032eec8d
This PR contains the theorem proving that signed division x.toInt / y.toInt only overflows when `x = intMin w` and `y = allOnes w` (for `0 < w`). To show that this is the *only* case in which overflow happens, we refer to overflow for negation (`BitVec.sdivOverflow_eq_negOverflow_of_neg_one`): in fact, `x.toInt/(allOnes w).toInt = - x.toInt`, i.e., the overflow conditions are the same as `negOverflow` for `x`, and then reason about the signs of the operands with the respective theorems. These BitVec theorems themselves rely on numerous `Int.ediv_*` theorems, that carefully set the bounds of signed division for integers. co-authored by @bollu, @tobiasgrosser |
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