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Theorem no-leading-zero-04

⊦ b2i(by) < 0 → int2bytes(i) ≠ i2b(~1) ' + by ' + bytes

Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by: int2bytes-len-le-neg-01, int2bytes-len-le-neg-03,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 19
Proof steps: 37
Used lemmas: int2bytes-not-neg-01, int2bytes-minus-256-01, int2bytes-byte-neg, int2bytes-byte, int2bytes-minus-one, int2bytes-last-01, int2bytes-rec-neg-256-01, int2bytes-rec-neg-256,
Used spec theorems:
- int-div/div-eq-zero-01
- int-abs/Abs-neg
- int-abs/les
- int-basic2/neq
- list-last/bytelist/splitlasteq
- int-div/div-le-same-neg
Used simplifier rules:
- int-abs/neg-01
- int-div/neg-01
- int-div/abs
- list/bytelist/app-03
- list/bytelist/in-16
- list/bytelist/inex
- byte/notequal
- int-abs/forward-le
- int-abs/numlsledel-01
- list/bytelist/Last
- byte/byte
- int-abs/anti
- byte/bib-lower
- int-abs/numleledel-01
- list/bytelist/e
- list/bytelist/app-02-ant
- list-last/bytelist/bapp
- list-last/bytelist/l-05
- list-last/bytelist/l-in
- list/bytelist/e-01
- list-last/bytelist/lin-02
- int-abs/numls-03
- int-abs/mone-08
- int-mult/zero-gr
- int-abs/lels-04
- int-abs/minus-add
- int-mult/zero-neq-01
- int-div/nummult-ls-01
- int-div/nummult-ls
- list/bytelist/in-12
- int-abs/lels-02
- int-mult/commutativity
- int-mult/associativity
- int-abs/numadd-01
- int-mult/numeq-04
- int-div/div-elim-negpos
- int-abs/numsub
- int-div/div-ls-same
- list/bytelist/app-01
- list/bytelist/c-03
- int-abs/zero-gels-03
- int-abs/forward-lele
- int-abs/forward-le-04
- int-abs/numle-03
- int-div/div-ls-zero
- int-abs/forward-lels
- int-abs/le-add-03
- int-basic2/add-zero
- int-abs/neg-15
- int-abs/minus-02
- int-abs/neg-06
- int-abs/Abs-pos
- int-abs/sub-add-01
- int-abs/sub-le-01
- int-abs/leone
- int-abs/sub-ls
- int-abs/lsone
- int-div/div-lezero
- int-basic1/numlslsdel
- int-abs/zero-gels-01
- int-abs/forward-lsle
- int-abs/forward-le-01
- int-abs/neg-07
- intnat/labs
- list/bytelist/ni
- int-abs/abs-08
- int-abs/neg-13
- int-abs/numls-02
- int-basic1/ls-01
- int-basic2/add-a
- int-basic2/add-c
- int-abs/sub-eq
- list/bytelist/app-06
- list/bytelist/app
- list/bytelist/in-15
- list/bytelist/in-17
- list/bytelist/in-append
- int-basic1/numlsf
- int-abs/lels-03
- int-abs/lels-01
- int-abs/lels
- int-abs/forward-le-02
- list/bytelist/a
- list/bytelist/in-14