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Theorem uint2bits-len

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

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by: int2bits-len-neg, int2bits-len-pos, int2int-neg, uint2bits-len-max, uint2bits-len-min,
Used by units in proved state: bytes,
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 8
Proof steps: 17
Used lemmas: uint2bits-one, uint2bits-rec-01,
Used spec theorems:
Used simplifier rules:
- nat-basic2/eq-01
- intnat/rax-04
- int-abs/numsub
- int-abs/sub-add-01
- int-abs/lels-04
- int-basic2/pred
- int-mult/ls-pos
- int-basic1/irref
- int-mult/zero-gr
- int-mult/commutativity
- int-mult/associativity
- int-div/nummult-ls-02
- int-abs/lels-03
- int-abs/mone-06
- int-abs/numls-02
- int-abs/elim-sub
- int-basic1/two-ls
- nat-basic2/c
- nat-basic2/a
- list/bitlista/app
- list/bitlista/c
- list-data/bitlista/lf-01
- nat/add-num-04
- int-abs/Sub-def
- int-abs/anti
- int-abs/leone
- int-abs/sub-le-01
- intnat/labs
- int-div/abs
- int-abs/abs-16
- int-div/div2-nle
- list/bitlista/Last
- int-abs/lels
- int-abs/forward-lele
- int-pot/two-lez
- int-abs/lels-01
- int-basic1/lf-02
- int-basic1/lf-01
- int-basic1/trans
- list/bitlista/Two
- list/bitlista/len
- list/bitlista/len-02
- list/bitlista/a
- int-basic1/numlsf
- int-abs/numlsf-01
- int-basic1/lf-03
- int-abs/bet-01
- int-pot/two-leone
- int-abs/numle-02
- intnat/num-i2n-eq
- int-abs/numadd-01
- int-abs/lels-02
- int-abs/lsone
- int-basic1/ls-01
- int-basic2/add-c
- int-basic2/add-a
- int-abs/ler
- int-abs/succ-02
- int-pot/ls-pos
- int-abs/forward-lels