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Theorem bib-neg-high

⊦ i < 0 ∧ ~128 ≤ i % 256 → b2i(i2b(i)) = i % 256

Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by: bib-lower, bib-ls-same, bib-ls-same-01, byte-law-neg, byte-mult, byte-mult-neg, getsetShort-theorem,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 32
Proof steps: 55
Used lemmas: bib-bitlength, byte, num-i2b-neg, num-ibbi,
Used spec theorems:
Used simplifier rules:
- int-abs/forward-le-05
- int-basic1/forward-pos
- int-div/mod-grz
- nat/not-zero
- nat-basic1/lf-02
- bitopsaux/fill-nls
- int2bits/int2int-inj
- int2bits/int2bits-first-01
- int2bits/int2bits-fillfirst
- int-abs/numleledel-01
- int-abs/mone-08
- int2bits/int2bits-mone-02
- bitopsaux/fill-rec-one
- bitlista/mklist-num-01
- list/bitlista/len
- list/bitlista/len-02
- nat-basic2/a
- nat-basic2/c
- int2bits/int2bits-not-empty
- list-data/bitlista/l
- nat-basic1/f
- nat/lels-01
- int-basic1/numlslsdel-01
- int2bits/int2bits-zero
- int2bits/bits2int-pos
- int2bits/bits2uint-zero
- int2bits/bits2uint-one-02
- int-mult/zero-ls
- int-abs/Abs-pos
- int-abs/Sub-def
- int-mult/eq-neg
- int-basic2/add-in
- int-mult/zero-neq-01
- int-mult/eq-one-neg
- list-last/bitlista/last-def
- bitopsaux/inv-in-01
- int2bits/uint2bits-onein-01
- int-abs/neg-06
- bitopsaux/inv-append
- int-div/mod-two-pred-02
- int-div/div2-odd-01
- int-abs/sub-ls-01
- int-mult/two-zero
- int2bits/uint2bits-one
- list/bitlista/Two
- bitopsaux/invert-zero
- bitopsaux/inv-one-01
- list/bitlista/c
- bitopsaux/succ-zero
- list/bitlista/Last
- bitopsaux/sgn-two-01
- list-last/bitlista/l
- int-abs/neg-15
- int-abs/minus-02
- int-basic1/ls-01
- list/bitlista/c-08
- list-del/bitlista/lastn-one
- list-del/bitlista/num-lastN
- list/bitlista/a
- list/bitlista/app
- list-last/bitlista/mk-zero
- bitlista/mklist-num
- int-mult/neq-two
- int-abs/sub-eq
- int-abs/lsone
- int-div/nummult-ls
- int-abs/sub-ls
- int-abs/mone-05
- int-div/nummult-le-01
- int-abs/sub-le
- int-abs/minus-add
- int-mult/associativity
- int-basic2/add-zero
- int-abs/numlsledel-01
- int-abs/lels-02
- int-basic1/numlsf
- int-abs/anti
- int-abs/lels
- int-abs/numls-02
- int-abs/neg-13
- int-mult/commutativity
- int-div/div-elim-negpos
- int-abs/forward-lele
- int-abs/forward-lels
- int-abs/numle-02
- int-abs/numadd-01
- int-abs/negeq
- int-abs/forward-le-04
- int-abs/numlsledel
- int-basic2/add-c
- int-basic2/add-a
- int-abs/numle-03
- int-abs/negle-07
- int-abs/abs-08
- int-abs/zero-gels-01
- int-div/mod-ls-same-02
- int-abs/forward-lsle
- int-abs/lels-01
- int-abs/zero-gels-03
- int-abs/forward-le-02