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Theorem uint2bits-succ

⊦ 0 ≤ j → uint2bits(j + 1) = sgn(false ' + uint2bits(j) +1)

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

View the proof

Infos about the proof

Proved?: Yes
Interactions: 10
Proof steps: 18
Used lemmas: uint2bits-sgn-false, uint2bits-rec, uint2bits-zero, uint2bits-one, uint2bits-pos-num, uint2bits-rec-01,
Used spec theorems:
- bitopsaux/sgn-last
- bitopsaux/sgn-last-01
Used simplifier rules:
- int-div/div-two-zero-01
- int-abs/numleledel-01
- list/bitlista/app-03
- int-div/modeven-pos
- int-basic2/add-zero
- int-div/div-add-pos
- int-div/mod-two
- bitopsaux/succ-zero
- bitopsaux/sgn-append
- bitopsaux/sgn-two
- list/bitlista/app-05
- bitopsaux/sgn-not-empty-01
- bitopsaux/succ-truein-01
- int-mult/ls-same
- int-abs/succ-02
- int-mult/numabs-01
- int-abs/abs-16
- intnat/labs
- int-mult/zero-ge
- int-abs/mone-06
- int-mult/zero-ge-add
- int-div/mod-two-02
- int-div/div-mult-03
- int-mult/succ-rmerge
- int-mult/commutativity
- int-mult/associativity
- int-mult/two-zero
- int-abs/numadd-01
- int-abs/lels-01
- int-basic1/ls-01
- int-div/div-elim-pos
- int-abs/numls-02
- int-basic2/add-a
- int-basic2/add-c
- int-basic1/lf-03
- int-basic1/lf-02
- int-abs/lels
- int-abs/anti
- list/bitlista/Two
- list/bitlista/Last
- bitopsaux/succ-rec
- bitopsaux/succ-one
- list/bitlista/a
- bitopsaux/sgn-base-02
- list/bitlista/app-01
- int-abs/lels-02
- bitopsaux/sgn-two-02