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Theorem int2bits-len-neg-01

⊦ i < 0 → # int2bits(i) = # int2bits(~ i - 1)

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by: int2bits-add-low, int2bits-lelen-03, int2bits-len-mon, int2bits-len-neg-02, int2bits-len-range, int2bits-lslen-03,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 3
Proof steps: 6
Used lemmas: int2bits-len-neg, int2bits-len-pos, int2bits-zero, uint2bits-one, int2bits-neg-num,
Used spec theorems:
- int-pot/exin2pot
Used simplifier rules:
- int-abs/negle-13
- int-abs/neg-07
- int-abs/lels-01
- int-abs/lels-04
- int-abs/lels-03
- int-basic1/numlsf
- int-basic2/ls
- int-basic2/succ-01
- int-basic1/trans
- int-basic1/lf-01
- int-mult/zero-gr
- int-basic2/ls-02
- int-mult/commutativity
- int-mult/associativity
- int-mult/one
- int-mult/numls-09
- int-basic2/ls-01
- int-abs/forward-lsle
- int-pot/succ
- list/bitlista/len-02
- bitopsaux/sgn-two-01
- list/bitlista/Last
- bitopsaux/succ-zero
- list/bitlista/a
- list/bitlista/c
- bitopsaux/inv-one-01
- bitopsaux/invert-zero
- list/bitlista/Two
- int-abs/mone-06
- int-abs/numls-02
- int-abs/neg-13
- int-abs/mone-05
- int-abs/numle-03
- int-abs/negle-07
- int-basic2/add-c
- int-basic2/add-a
- int-abs/mone-08
- int-abs/lels
- int-abs/numls-03
- int-abs/neg
- int-abs/subsub