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Theorem int2unit-inv-rest

⊦ 0 < i → bits2uint(bitsinvert(int2bits(i).rest)) = 2 ^ (n→i(# uint2bits(i)) - 1) - i + 1

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
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: int2int-rest, uint2bits-false, uint2bits-firstpos, uint2bits-eq, int2bits-pos, bits2uint-base, int2bits-not-empty, bits2uint-inv-pos,
Used spec theorems:
- Used simplifier rules:
  - bitopsaux/invert-base
  - int-abs/elim-sub
  - int-abs/lels-01
  - int-basic1/ls-01
  - list/bitlista/in-14
  - list/bitlista/app
  - list/bitlista/c
  - list/bitlista/a
  - list-data/bitlista/elim-list-c
  - int-abs/subsub
  - int-abs/sub-add-01
  - int-basic2/add-a
  - int-basic2/add-c
  - int-abs/neg-15
  - int-abs/sub-eq
  - int-abs/Sub-def
  - int-basic2/add-in