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Theorem int2bytes-first-zerobyte

⊦ 0 ≤ i → (int2bytes(i).first = i2b(0) ↔ n→i(# int2bits(i)) % 8 = 1)

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by: int2bytes-first-zerobyte-01, int2bytes-len-ls-01,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 18
Proof steps: 35
Used lemmas: int2bytes-byte, int2bytes-empty, int2bytes-le255, int2bytes-le127, int2bytes-rec-pos,
Used spec theorems:
Used simplifier rules:
- int-div/pos
- intnat/labs
- int-div/abs
- int-abs/abs-16
- int-div/num-ls
- int-mult/le-same
- int-mult/associativity
- int-mult/commutativity
- int-div/mod-less
- int-div/mod-zero-02
- bitopsaux/fill-rec-one
- bitlista/mklist-num
- list-last/bitlista/mk-zero
- list/bitlista/app
- list/bitlista/e-01
- list-last/bitlista/mk-len
- nat/lels-01
- nat/pred-03
- bitopsaux/fill-empty
- intnat/nat2int
- int-abs/numlsledel-01
- nat-basic2/c
- nat-basic2/a
- intnat/n2i-add
- list/bitlista/a
- list/bitlista/len
- int-div/div-zero-03
- int-basic1/ls-01
- nat-basic1/f
- nat-basic1/lf-02
- intnat/num-n2i-eq
- int-abs/numleledel-01
- int2bits/int2bits-not-empty
- list-data/bitlista/l
- nat/not-zero
- nat/lels
- intnat/num-n2i-ls
- intnat/abs-02
- int-basic1/lst
- int-abs/lels-02
- int2bits/int2bits-zero
- list/bitlista/len-02
- list/bytelist/first
- int-abs/numlsledel
- int-basic2/num-between
- byte/num-i2b-equal
- list/bytelist/a
- list/bytelist/c-08
- int-abs/numlelsdel-01
- int-abs/numleledel
- int-basic1/numlslsdel-01
- int-basic1/forward-pos
- int-abs/forward-le-05
- int-abs/lels-04
- int-abs/lels-01
- int-abs/lels
- int-abs/forward-le-01