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Theorem bits2int-le8

⊦ # bits ≤ 8 ∧ bits ≠ [] → ¬ bits2int(bits) < ~128

Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by: bits2int8,
Used by units in proved state: bytes,
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 9
Proof steps: 16
Used lemmas: bits2int-first-01, bits2bits-def, int2bits-len-neg,
Used spec theorems:
Used simplifier rules:
- int-abs/neg-13
- int-basic2/add-in
- intnat/i2i-pos
- intnat/n2i-add
- int-abs/sub-eq
- intnat/num-n2i-eq
- list-data/bitlista/lf-01
- bitopsaux/sgn-first-01
- list/bitlista/c
- list/bitlista/app
- list/bitlista/a
- bitopsaux/sgn-one-01
- int-abs/sub-ls-01
- intnat/num-n2i-ls-02
- int-abs/sub-le-01
- intnat/num-n2i-ls-06
- nat/lels-03
- nat-basic1/lf-01
- nat-basic1/f
- nat/fle-01
- list-data/bitlista/l
- bitopsaux/sgn-empty-01
- nat-basic2/l-01
- intnat/abs-zero
- nat-basic2/a
- nat-basic2/c
- nat/l-num-04
- bitopsaux/sgn-length
- int-abs/numlsf-01
- int-abs/numls-02
- int-div/nummult-ls-02
- int-abs/lels-01
- int-abs/lels-04
- int-basic2/lst-03
- int-basic2/ls
- int-mult/ls-same-01
- int-mult/zero-gr
- int-mult/commutativity
- int-mult/associativity
- int-mult/one
- int-mult/numls-08
- int-pot/succ
- int-abs/mone-06
- int-abs/lels-02
- int-basic2/add-zero
- int-abs/lsone
- int-abs/numle-02
- int-abs/mone-08
- int-abs/numls-03
- int-basic1/lf-03
- int-basic2/succ-01
- int-basic1/trans
- int-basic1/lf-01
- int-basic2/ls-02
- int-basic2/add-c
- int-basic2/add-a
- int-basic2/ls-01
- int-abs/forward-lsle
- int-abs/negle-13
- int-abs/neg-07
- int-abs/lels-03
- int-abs/lels
- int-basic1/numlsf