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Theorem uint2bits-pred

⊦ 0 < j → uint2bits(j - 1) = sgn(bitsinvert(bitsinvert(uint2bits(j)) +1))

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by: int2bits-pred, uint2bits-succ-intro,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 9
Proof steps: 16
Used lemmas: uint2bits-sgn-false-01, uint2bits-rec, uint2bits-pos-num, uint2bits-one, uint2bits-zero, uint2bits-rec-01,
Used spec theorems:
- bitopsaux/sgn-last-diff
Used simplifier rules:
- int-abs/mone-06
- int-abs/numls-02
- int-mult/zero-ge-add
- int-mult/neq-two
- int-abs/numadd-01
- int-div/mod-two-02
- int-div/div-mult-03
- int-abs/numsub
- bitopsaux/inv-inv
- bitopsaux/inv-in-01
- bitopsaux/succ-truein-01
- int-mult/zero-ge
- int-mult/zero-gr
- int-div/mod-two-03
- int-div/nummult-ls-02
- int-mult/eq-same
- int-basic2/add-c
- int-basic2/add-a
- int-basic2/add-zero
- int-abs/lels-01
- int-basic1/ls-01
- int-div/div-elim-pos
- int-div/div2-nle-01
- intnat/labs
- int-div/abs
- int-abs/abs
- int-div/num-ls
- int-mult/le-same
- int-mult/associativity
- int-mult/commutativity
- int-basic1/lf-03
- int-div/two-odd
- int-div/mod-two-05
- bitopsaux/inv-one
- bitopsaux/inv-append
- int-abs/numlsf-01
- int-abs/sub-ls-01
- int-abs/lels
- int-abs/bet
- int-abs/sub-eq
- list/bitlista/Two
- bitopsaux/invert-zero
- bitopsaux/inv-one-01
- list/bitlista/c
- list/bitlista/a
- bitopsaux/succ-zero
- list/bitlista/Last
- bitopsaux/invert-one
- bitopsaux/sgn-two
- list/bitlista/c-04
- bitopsaux/inv-false
- bitopsaux/succ-rec
- bitopsaux/sgn-rec
- bitopsaux/sgn-two-02
- list/bitlista/app-01