max/lean4-htt
1
0
Fork 0
Code Issues Pull requests Projects Releases Packages Wiki Activity Actions 2

feat: bitblasting theorems about unsigned bitvector inequalities (#4178)

Browse source 
This PR adds theorems that relate unsigned bitvector comparisons
`BitVec.ult` and `BitVec.ule` to `BitVec.carry`. These lemmas are a
prerequisite to bit-blasting these comparisons in LeanSAT.
This commit is contained in:
Alex Keizer 2024-05-16 02:01:31 +02:00 • committed by GitHub
parent 8204b79b3c
commit 2a966b46f2
No known key found for this signature in database
GPG key ID: B5690EEEBB952194
1 changed files with 14 additions and 0 deletions
Show stats Download patch file Download diff file Expand all files Collapse all files

14
src/Init/Data/BitVec/Bitblast.lean
View file

@ -184,4 +184,18 @@ theorem bit_neg_eq_neg (x : BitVec w) : -x = (adc (((iunfoldr (fun (i : Fin w) c
simp [← sub_toAdd, BitVec.sub_add_cancel]
· simp [bit_not_testBit x _]
/-! ### Inequalities (le / lt) -/
theorem ult_eq_not_carry (x y : BitVec w) : x.ult y = !carry w x (~~~y) true := by
simp only [BitVec.ult, carry, toNat_mod_cancel, toNat_not, toNat_true, ge_iff_le, ← decide_not,
Nat.not_le, decide_eq_decide]
rw [Nat.mod_eq_of_lt (by omega)]
omega
theorem ule_eq_not_ult (x y : BitVec w) : x.ule y = !y.ult x := by
simp [BitVec.ule, BitVec.ult, ← decide_not]
theorem ule_eq_carry (x y : BitVec w) : x.ule y = carry w y (~~~x) true := by
simp [ule_eq_not_ult, ult_eq_not_carry]
end BitVec