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Theorem bib-pos-low

⊦ 0 ≤ i ∧ i % 256 ≤ 127 → b2i(i2b(i)) = i % 256

Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by: bib-ls-same, bib-ls-same-01, byte-law-add-pos, byte-law-div-not, byte-law-neg, byte-mult, byte-mult-pos, getsetShort-theorem, out-test-08,
Used by units in proved state: bytes,
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 10
Proof steps: 21
Used lemmas: num-i2b-pos, num-ibbi,
Used spec theorems:
Used simplifier rules:
- int-abs/absle
- int-abs/forward-lele
- int-abs/numleledel
- int-basic1/numlsf
- int-div/mod-ls-zero
- list/bitlista/in-17
- list/bitlista/in-append
- list/bitlista/in-14
- list/bitlista/c
- list-del/bitlista/lastN-empty
- list-data/bitlista/elim-list-c
- int-basic2/add-zero
- int-mult/zero-eq
- list/bitlista/rest
- list/bitlista/app
- list/bitlista/a
- int-div/nummult-ls-02
- list/bitlista/len-02
- int2bits/int2bits-not-empty
- list-data/bitlista/l
- nat/not-zero
- bitopsaux/fillsgn-longer
- nat/lels
- int2bits/int2bits-fillfirst
- int2bits/int2bits-first-02
- int-abs/lels-03
- int-abs/lels-04
- int-mult/commutativity
- int-mult/associativity
- int-mult/zero-gr
- int-basic2/ls-02
- int-abs/numlsledel
- int-basic2/add-c
- int-basic2/add-a
- int-basic1/ls-01
- int-div/div-elim-pos
- int-basic1/lst
- int-abs/lels-02
- int2bits/int2bits-zero
- nat/lels-01
- int-abs/anti
- int-abs/lels
- int-basic1/numlslsdel-01
- int-abs/forward-lels
- int-basic1/forward-pos
- int-abs/forward-le-05
- int-abs/lels-01
- int-abs/numleledel-01
- int-abs/forward-le-01