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Theorem bits2int-sign

bits ≠ [], ¬ (¬ bits.first) ∈ bits0 ⊦ bits2int(bits0 + bits) = bits2int(bits)

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by: bits2int-mklist, bits2int-mklist-01, bits2int-ones-01, bits2int-sgn,
Used by units in proved state: intops,
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 5
Proof steps: 19
Used lemmas: bits2uint-zeros-02, bits2uint-zeros-03, bits2int-pos, bits2int-neg-01, bits2int-neg, bits2int-pos-01,
Used spec theorems:
- Used simplifier rules:
  - bitopsaux/invert-zero
  - list/bitlista/c-07
  - bitopsaux/inv-in-02
  - list/bitlista/e-03
  - int-basic2/add-zero
  - int-abs/sub-eq
  - int-basic2/add-c
  - int-basic2/add-a
  - int-abs/neg-15
  - bitopsaux/succ-prefix
  - bitopsaux/inv-append
  - list/bitlista/rest-01
  - list/bitlista/in-06
  - list/bitlista/first-01
  - int-abs/negeq
  - bitopsaux/invert-one
  - list/bitlista/e
  - list/bitlista/app-02-ant
  - list/bitlista/c-08
  - list/bitlista/Nil
  - list/bitlista/a
  - list/bitlista/e-01
  - list/bitlista/c
  - list-data/bitlista/elim-list-c