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Theorem uint2bits-len-mon

⊦ 0 ≤ i ∧ i ≤ j → # uint2bits(i) ≤ # uint2bits(j)

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by: bits2uint-nle, int2bits-less-2pot, uint2bits-len-mon-01, uint2bits-len-mon-02,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 5
Proof steps: 10
Used lemmas: uint2bits-one, uint2bits-zero, uint2bits-rec-01, uint2bits-empty,
Used spec theorems:
- Used simplifier rules:
  - int-mult/le-same
  - int-abs/abs-16
  - int-div/abs
  - intnat/labs
  - nat/lels
  - int-div/num-ls
  - nat/fle
  - nat/fle-01
  - nat-basic1/ref-1
  - int-basic1/lf-01
  - int-basic1/trans
  - int-abs/forward-lels
  - int-div/nummult-ls-02
  - int-mult/associativity
  - int-mult/commutativity
  - int-mult/zero-gr
  - int-div/ls-same-pos-02
  - nat-basic2/l
  - nat/l-num-05
  - nat-basic1/one-01
  - nat-basic2/a
  - nat-basic2/c
  - int-abs/leone
  - nat-basic2/l-02
  - int-abs/forward-lsle
  - int-basic1/lf-02
  - int-basic1/lst
  - int-div/div-two-zero-01
  - list/bitlista/Last
  - int-abs/zeroone
  - list/bitlista/len
  - list/bitlista/Two
  - list/bitlista/first
  - list/bitlista/c-04
  - list/bitlista/a
  - list/bitlista/app
  - list/bitlista/c
  - list-data/bitlista/lf-01
  - nat-basic1/one
  - list/bitlista/len-02
  - int-abs/lels-02
  - int-abs/anti
  - int-abs/lels
  - int-abs/lels-01
  - int-abs/lels-04
  - list-data/bitlista/l
  - int-abs/forward-lele
  - nat-basic1/f
  - nat/lels-01