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Theorem int2bits-neg-03

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

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by: int2bits-add-high, int2bits-add-low, int2bits-neg-02, uint2bits-add-high,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 20
Proof steps: 38
Used lemmas: int2bits-sgn, uint2bits-zero, uint2bits-eq, uint2bits-onein, uint2bits-empty, int2bits-less-2pot, uint2bits-one, uint2bits-rec-01, int2bits-neg, int2bits-pos, int2bits-not-empty, bits2int-inj, int2int-neg,
Used spec theorems:
Used simplifier rules:
- int-mult/ls-same
- int-basic1/lf-02
- int-basic2/ls
- int-abs/zeroone
- int-abs/anti
- bitopsaux/succ-empty-01
- bitopsaux/succ-truein-01
- int-div/div-two-zero-01
- int-abs/mone-08
- list/bitlista/in-17
- bitopsaux/inv-in
- list/bitlista/in-append
- list/bitlista/e-02
- list/bitlista/app-02-ant
- bitopsaux/inv-empty
- int-abs/forward-lels
- int-div/div-lezero
- list/bitlista/e
- bitopsaux/inv-one
- bitopsaux/inv-append
- int-div/mod-neg-01
- int-div/neg-01
- int-mult/commutativity
- int-abs/subsub
- int-abs/neg-15
- int-abs/sub-add-09
- int-abs/neg-02
- int-mult/numsucc
- int-mult/associativity
- int-mult/zero-gr
- int-abs/sub-ls-01
- int-mult/ls-add
- int-pot/grz
- 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-basic1/ls-01
- list/bitlista/c-04
- bitopsaux/sgn-two-01
- list/bitlista/Last
- bitopsaux/succ-zero
- bitopsaux/inv-one-01
- bitopsaux/invert-zero
- list/bitlista/Two
- int-basic1/lf-03
- int-abs/numadd-01
- int-abs/negeq
- int-basic2/add-a
- int-abs/neg
- int-abs/abs-08
- int-abs/lels-01
- list/bitlista/a
- list/bitlista/app
- list/bitlista/c
- list-data/bitlista/elim-list
- bitopsaux/sgn-empty
- int-basic2/add-c
- int-abs/lels
- int-abs/lels-03