lean4-htt/src/Std/Tactic
Luisa Cicolini bc032eec8d
feat: add BitVec.sdivOverflow definition and lemmas for overflow in signed and unsigned division (#7671)
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
2025-04-24 15:27:18 +00:00
..
BVDecide feat: add BitVec.sdivOverflow definition and lemmas for overflow in signed and unsigned division (#7671) 2025-04-24 15:27:18 +00:00
BVDecide.lean feat: import LeanSAT's tactic frontends 2024-08-28 18:14:39 +02:00