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Theorem uint2bits-falsein-01

⊦ 0 < j → (false ∈ uint2bits(j).rest ↔ ¬(∃ i. j = 2 ^ i - 1))

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by: int2bits-add-high, int2bits-falsein-02,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 15
Proof steps: 25
Used lemmas: uint2bits-empty, uint2bits-one, uint2bits-rec-01,
Used spec theorems:
- list/bitlista/rest-01
- int-pot/two-mod-01
- int-pot/Pot-pos
- int-pot/two-minus
- int-pot/succ
Used simplifier rules:
- int-pot/two-minus
- int-basic2/zero-04
- int-abs/anti
- int-mult/eq-one
- int-abs/forward-le-04
- int-abs/sub-pred
- int-mult/eq-pos
- int-mult/zero-ge-add
- int-mult/zero-ge
- int-abs/mone-06
- int-abs/numls-02
- int-mult/two-zero
- int-abs/numadd-01
- int-mult/commutativity
- int-mult/associativity
- int-mult/succ-rmerge
- int-abs/forward-le-01
- int-abs/lels-02
- int-basic1/ls-01
- int-div/div-elim-pospos
- int-basic1/two-ls
- int-div/div-lezero
- intnat/labs
- int-div/abs
- int-abs/abs-16
- int-div/div2-nle
- int-abs/Sub-def
- int-basic2/add-a
- int-basic2/add-c
- int-basic1/lst-01
- int-abs/lsone
- int-abs/sub-ls-01
- int-pot/pot2-pos-01
- int-abs/lenls
- list/bitlista/in-append
- int-basic1/lst
- int-abs/lels-01
- int-div/div-two-zero-01
- list/bitlista/Last
- int-abs/lels
- int-abs/lels-03
- list/bitlista/Two
- list/bitlista/c-07
- list/bitlista/a
- list/bitlista/in-17
- int-pot/eq2
- int-abs/forward-le-05
- int-abs/sub-eq