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Theorem rightshift-8-01-01

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

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 33
Proof steps: 63
Used lemmas: bytes2int-first-gez, bytes2int-mklist-mones-01, bytes2int-first-lez, bytes2int-mklist-zeros-01, fillsgn-longer, int2bytes-byte, int2bytes-len-le-neg-03, int2bytes-len-le-neg-02, bytes2int-mklist-mones, int2bytes-len-ls-upper, int2bytes-len-le-upper, bytes2int-mklist-zeros, fillsgn-pos, int2bytes-empty, int2int, fillsgn-neg, rightshift-8-01,
Used spec theorems:
- intops/shiftright-pos-div-01
- nat/prop-01
- list-del/bytelist/first-append
- intops/shiftright-neg-mone
- intops/shiftright-neg-div-01
- intops/shiftright-neg-div-02
- int-div/div-zero-02
- int-abs/add-rew
- int-div/mod-neg-01
- int-pot/two-zero
- int-div/modex
- int-mult/zero-ls
- int-mult/zero-ge
- list-del/bytelist/firstn-app-01
- list-del/bytelist/firstn-first
Used simplifier rules:
- nat/zero-01
- list-del/bytelist/firstN-empty
- nat/lels-03
- nat-basic1/ls-02
- nat/eq-01
- list-del/bytelist/first-all
- nat/ge
- nat/sub-base
- nat-basic1/f
- int-basic1/lst-01
- int-abs/numle-02
- int-abs/mone-08
- int-abs/lels-02
- int-mult/zero-ls-03
- int-mult/zero-ge-01
- int-abs/numle-03
- int-abs/mone-05
- int-basic1/ls-01
- int-mult/succ-rmerge
- int-div/div-mult-03
- int-basic2/ls
- int-pot/two-lsz
- byte/notequal
- list/bytelist/first
- int-div/mod-same
- int-abs/neg-05
- int-basic2/add-zero
- int-abs/sub-ls
- int-abs/neg-15
- int-abs/neg-06
- int-abs/forward-le-04
- int-abs/anti
- int-abs/neg-13
- int-abs/abs-08
- int-abs/sub-eq
- int-mult/zero-eq
- int-abs/neg-07
- int-pot/pot2-ls-pred
- int-basic2/ls-01
- int-abs/zero-gels-01
- int-abs/forward-lsle
- int-abs/lels-03
- int-abs/negle-13
- int-abs/forward-le-02
- intnat/ini2-abs
- int-abs/forward-le-05
- int-abs/forward-lels
- int-pot/pot2-pos
- int-abs/sub-le-01
- int-abs/leone
- int-mult/zero-gr
- int-abs/abs-06
- int-abs/abs-03
- int-mult/zero-ge
- int-pot/ls-pos-2pot-01
- int-abs/sub-ls-01
- int-mult/numls-02
- int-mult/Mult-zero
- int-basic2/add-a
- int-basic2/add-c
- int-pot/abs-2pot
- int-abs/absle
- int-mult/commutativity
- int-mult/associativity
- int-mult/abs-eqall
- list-del/bytelist/first-mklist
- list-last/bytelist/mk-len
- nat/lels-01
- nat/le-ls-simp
- int-abs/zero-gels-04
- nat-basic2/l-01
- nat/add-01
- int-abs/lels-01
- int-abs/lels-04
- int-abs/forward-le-01
- list-data/bytelist/l
- nat/lez-01
- nat-basic2/z
- intops/rightshift-zero
- int-abs/lels
- nat-basic2/c
- nat-basic2/a
- intnat/abs-zero
- nat/le-add
- nat/lels