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Theorem ubits2ubits-def

⊦ uint2bits(bits2uint(bits)) = sgn(false ' + bits)

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by: bits2bits-def, bits2uint-nle, int2bits-bits2unit-01, ubits2ubits-neg, ubits2ubits-pos,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 16
Proof steps: 28
Used lemmas: uint2bits-one, uint2bits-empty, bits2uint-not-neg-01, bits2uint-zeros, bits2uint-not-zero, bits2uint-not-neg, uint2bits-rec, bits2uint-zero, bits2uint-rec-02, uint2bits-zero, bits2uint-base,
Used spec theorems:
- list/bitlista/lastdiv-rew
- bitopsaux/sgn-last
- bitopsaux/sgn-zero
- int-div/div-two
- bitopsaux/sgn-last-01
Used simplifier rules:
- int-div/mod-two-04
- list/bitlista/in-10
- list/bitlista/Two
- int-basic2/add-c
- int-basic2/add-a
- int-mult/zero-gr
- int-abs/numls-02
- list/bitlista/app-03
- bitopsaux/sgn-append
- bitopsaux/sgn-two
- list/bitlista/app-05
- int-abs/lels-01
- list/bitlista/len
- list/bitlista/len-02
- nat-basic2/s
- nat-basic1/ref-1
- nat-basic2/a
- nat-basic2/c
- list/bitlista/Last
- int-div/mod-two-02
- int-div/div-mult-03
- list/bitlista/in-append
- list/bitlista/in-17
- list/bitlista/app-02-ant
- list/bitlista/e
- int-mult/commutativity
- int-mult/associativity
- int-abs/lels
- int-div/nummult-ls-02
- list/bitlista/app
- list/bitlista/a
- bitopsaux/sgn-one
- list/bitlista/c-04