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Theorem rightshift-8-01

⊦ i→n(j) < # int2bytes(i) → i >> 8 * j = bytes2int(firstn(# int2bytes(i) - i→n(j), int2bytes(i)))

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by: int2bytes-index-rightshift, rightshift-8-01-01,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 47
Proof steps: 86
Used lemmas: bytes2int-zero, int2bytes-le127, int2bytes-le255, int2bytes-rec-pos, int2bytes-minus-256, int2bytes-rec-neg-256, int2bytes-last-01, bytes2int-one, int2bytes-byte, int2bytes-byte-neg, int2bytes-rec-neg-256-01, int2int, int2bytes-empty,
Used spec theorems:
Used simplifier rules:
- int-abs/minus-02
- int-abs/neg-15
- int-abs/forward-lsle
- int-div/div-eq-zero
- int-abs/numlsledel
- int-basic1/numlslsdel-01
- int-basic1/forward-pos
- int-abs/lels-04
- int-abs/numleledel
- int-abs/forward-le-01
- int-div/nummult-ls-01
- int-div/nummult-ls-03
- int-abs/mone-06
- int-abs/numlsledel-01
- intops/shiftright-zero
- int-abs/forward-le-05
- int-basic1/two-ls
- int-abs/lels-02
- int-abs/absle
- intnat/num-i2n-ls-01
- int-abs/subsub
- int-mult/minus-left
- int-basic1/minus-one
- list-last/bytelist/butlast-def
- nat-basic2/l
- nat/ls-01
- nat/le-add
- nat/not-zero
- int-abs/abssub
- intnat/abs
- nat/lels-01
- nat/ls-02
- nat/succ-01
- nat/le-ls-simp
- intnat/labs-01
- nat/let
- int-abs/abs-10
- int-abs/sub-le-01
- int-abs/lep-01
- intnat/labs
- nat/add-01
- nat-basic2/c
- nat-basic2/a
- nat/lels
- nat-basic2/s
- int-basic1/ls-01
- int-basic1/lst-01
- int-abs/Abs-pos
- intnat/num-i2n-eq-01
- int-abs/negeq
- int-abs/numadd-01
- int-abs/abs-08
- int-abs/neg-13
- int-abs/numls-02
- int-abs/numlelsdel-01
- int-basic2/add-a
- int-basic2/add-c
- int-abs/sub-eq
- int-abs/sub-eq-01
- byte/num-ibbi
- list-del/bytelist/firstn-one
- nat-basic1/lf-02
- list/bytelist/a
- list/bytelist/len
- list/bytelist/len-02
- int-basic1/numlslsdel
- nat-basic1/one-01
- intnat/abs-zero
- int-abs/numleledel-01
- int-abs/anti
- int-abs/forward-lels
- int-mult/pred-rmerge
- int-abs/lels
- int-abs/lels-03
- int-abs/forward-le-02
- list-del/bytelist/first-all
- nat/sub-base
- intops/rightshift-zero
- int-abs/abs-06
- int-abs/leone
- int-div/nummult-le-02
- int-abs/lels-01
- int-mult/commutativity
- int-mult/associativity
- int-mult/abs-eqall
- list-data/bytelist/l
- nat-basic1/f