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Theorem uint2bits-len-max

0 ≤ i, 0 ≤ j, j < 2 ^ i ⊦ # uint2bits(j) ≤ i→n(i + 1)

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by: int2bits-rec-2pot-neg-02,
Used by units in proved state: bytes,
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 3
Proof steps: 6
Used lemmas: uint2bits-len, uint2bits-zero, uint2bits-empty,
Used spec theorems:
- int-pot/exin2pot
- intnat/add-01
Used simplifier rules:
- nat/l-num-01
- nat-basic2/s
- intnat/labs
- int-abs/absle
- int-abs/abs-16
- int-abs/numadd-01
- intnat/abs-zero
- int-abs/lels-03
- int-abs/numlsf-01
- int-abs/ler
- int-abs/succ-02
- int-pot/ls-pos
- int-basic1/trans
- int-basic1/lf-01
- int-abs/lels-02
- nat-basic2/c
- nat-basic2/a
- nat-basic2/l-02
- list/bitlista/len-02
- int-abs/anti
- int-abs/lels
- int-abs/lels-01
- int-abs/lels-04
- list-data/bitlista/l
- int-abs/forward-lels
- nat-basic1/f
- nat/lels-01
- int-basic2/add-c
- int-basic2/add-a
- intnat/rax-04