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Theorem bits2int-inv

⊦ bits ≠ [] → bits2int(bitsinvert(bits)) = ~ bits2int(bits) - 1

Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by: int2bits-rec-2pot-neg-02,
Used by units in proved state: intops,
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 3
Proof steps: 10
Used lemmas: bits2uint-zeros-03, bits2uint-succ, bits2int-neg, bits2int-pos, bits2int-pos-02,
Used spec theorems:
- Used simplifier rules:
  - bitopsaux/inv-inv
  - bitopsaux/invert-zero
  - bitopsaux/inv-empty
  - list/bitlista/e
  - list/bitlista/app-02-ant
  - int-basic2/add-in
  - int-abs/mone-01
  - int-abs/sub-eq
  - int-abs/neg-15
  - bitopsaux/invert-one
  - list/bitlista/a
  - list/bitlista/e-01
  - list/bitlista/c
  - list-data/bitlista/elim-list-c
  - int-basic2/add-c
  - int-basic2/add-a
  - int-abs/numadd-01
  - int-abs/negeq
  - int-abs/subsub