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Theorem int2int-neg

⊦ j < 0 → bits2int(int2bits(j)) = bits2int(int2bits(2 ^ n→i(# int2bits(~ j)) + j).rest)

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by: int2bits-neg-03,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 21
Proof steps: 39
Used lemmas: uint2bits-one, uint2bits-pos-num, uint2bits-2pot-01, uint2bits-len-01, uint2bits-2pot, uint2bits-len, uint2bits-empty-01, int2bits-not-empty, uint2bits-zero, uint2int-rest, int2bits-less-2pot, int2int-inj, int2bits-pos,
Used spec theorems:
Used simplifier rules:
- list/bitlista/Last
- list/bitlista/Two
- int-abs/sub-ls
- int-mult/numsucc
- int-abs/neg-05
- int-pot/two-zero
- int-mult/two-zero
- int-mult/pred-rmerge
- int-abs/neg-03
- int-abs/numlef
- int-abs/numls-02
- int-abs/numle-02
- int-mult/ls-same-02
- int-basic1/numlsf
- int-mult/le-pos
- int-mult/zero-le
- int-mult/le-same
- int-mult/modzero-01
- int-basic2/lst-04
- int-mult/ls-pos
- int-mult/zero-ls
- int-abs/numls-03
- int-mult/numls-01
- int-mult/numls-02
- int-abs/neg-07
- int-mult/numle-01
- int-abs/negeq
- int-abs/neg-15
- int-mult/dist-sub-merge
- list/bitlista/len
- list/bitlista/len-02
- list-last/bitlista/mk-len
- list/bitlista/a
- intnat/n2i-add
- intnat/i2i-pos-01
- nat-basic2/a
- nat-basic2/c
- int-abs/numsub
- int-mult/eq-pos
- int-abs/negle-13
- int-mult/dist-rmerge
- int-basic2/zero-02
- int-abs/sub-le
- int-mult/minus-one-01
- int-pot/two-lsz
- int-mult/ls-same-01
- int-mult/le-same-01
- int-abs/lep-01
- int-mult/zero-ge
- int-mult/numls-08
- int-mult/numle-08
- int-abs/succ-02
- int-abs/numls-01
- int-abs/absle
- int-abs/abs-12
- intnat/ini2-abs
- int-abs/lels-04
- int-abs/lep
- list-data/bitlista/l
- nat-basic1/z
- intnat/num-n2i-ls-02
- intnat/nat2int
- int-mult/zero-gr
- int-div/nummult-ls-02
- int-pot/ls-pos
- int-mult/one
- int-mult/numls-09
- int-pot/two-le
- int-abs/lep-02
- int-abs/forward-lels
- int-abs/forward-lele
- int-pot/succ
- int-abs/lels-03
- int-abs/neg
- int-basic2/add-in
- int-abs/sub-eq
- int-mult/ls-same
- int-basic2/ls
- int-basic1/lf-03
- list/bitlista/rest
- int-basic1/lf-02
- int-abs/zeroone
- int-abs/anti
- int-abs/lels
- int-pot/grz
- int-mult/ls-add
- int-mult/associativity
- int-mult/commutativity
- int-basic2/lst-03
- int-abs/forward-lsle
- int-abs/elim-sub
- int-abs/numlsf-01
- int-basic2/ls-02
- int-basic2/ls-01
- int-basic2/succ-01
- int-basic1/trans
- int-basic1/lf-01
- int-abs/neg-13
- int-abs/negle-07
- int-basic2/add-zero
- int-basic2/add-a
- int-basic2/add-c
- int-basic1/ls-01
- int-abs/lels-01