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Theorem uint2uint-inv

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

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by: uint2int-rest, uint2uint-inv-01,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 5
Proof steps: 8
Used lemmas: bits2uint-rec-02, bits2uint-one-03, bits2uint-zero, uint2bits-one, uint2bits-rec-01,
Used spec theorems:
- int-pot/succ
Used simplifier rules:
- int-div/div2zero
- int-mult/succ-rmerge
- int-mult/eq-dist
- int-div/div2one-01
- int-basic2/add-a
- int-basic2/add-c
- int-mult/associativity
- int-mult/commutativity
- int-basic2/add-in
- intnat/nat2int
- int-basic1/two-ls
- int-div/div-lezero
- intnat/labs
- int-div/abs
- int-abs/abs-16
- int-div/div2-nle
- bitopsaux/inv-one
- bitopsaux/inv-append
- nat-basic2/c
- nat-basic2/a
- intnat/n2i-add
- list/bitlista/Last
- int-abs/lels
- int-abs/lels-03
- int-basic1/lf-02
- list/bitlista/Two
- list/bitlista/len
- list/bitlista/len-02
- list/bitlista/a
- bitopsaux/invert-zero
- bitopsaux/inv-one-01
- list/bitlista/c
- int-abs/sub-eq