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Theorem bits2bits-def

bits ≠ [] ⊦ int2bits(bits2int(bits)) = sgn(bits)

Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by: bits2bits-invert, bits2int-inj, bits2int-le8, bits2int-le8-01, int2int-lastn-negpos,
Used by units in proved state: intops, bytes, byte,
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 12
Proof steps: 26
Used lemmas: bits2uint-not-neg-01, int2bits-pos, bits2uint-one, ubits2ubits-def, bits2uint-zeros, bits2uint-not-zero, int2bits-zero, bits2uint-not-neg, int2bits-neg, bits2int-neg, bits2int-pos-01,
Used spec theorems:
Used simplifier rules:
- int-abs/lels-01
- list/bitlista/in-06
- bitopsaux/sgn-zeros
- bitopsaux/succ-zero
- list/bitlista/Last
- bitopsaux/sgn-sgn-01
- list/bitlista/in-empty
- int-basic2/add-c
- int-basic2/add-a
- int-mult/commutativity
- int-mult/associativity
- int-mult/zero-ge
- int-abs/mone-06
- int-abs/numls-02
- list/bitlista/app
- bitopsaux/invert-base
- bitopsaux/inv-in-02
- list/bitlista/in-10
- list/bitlista/in-append
- list/bitlista/app-01
- bitopsaux/succ-zeros
- bitopsaux/inv-append
- list/bitlista/in-13
- list/bitlista/neq
- bitopsaux/succ-zero-02
- bitopsaux/inv-in-01
- bitopsaux/succ-zero-01
- bitopsaux/succ-one
- bitopsaux/inv-inv
- bitopsaux/sgn-base-01
- bitopsaux/succ-prefix
- bitopsaux/succ-zeros-01
- bitopsaux/sgn-rec
- bitopsaux/invert-zero
- int-abs/abs-16
- int-abs/abs-neg
- bitopsaux/succ-truein-01
- int-abs/lels
- int-abs/neg-05
- bitopsaux/invert-one
- list/bitlista/a
- list/bitlista/e-01
- list/bitlista/c
- list-data/bitlista/elim-list-c