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Theorem and-com

⊦ bits ≠ [] ∧ bits0 ≠ [] → bitsand(bits, bits0) = bitsand(bits0, bits)

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by: add-ones-grlen-01, add-ones-lelen-01, and-one-01, band-associativity, band-bitlength, band-commutativity, band-min-01, band-min-02, bitsand-cast, bitsand-cast-01, bitsand-cast-04, bitsand-cast-05, bor-2pot-plus, bor-2pot-plus-01, bor-notAndNot, bxor-def-logic,
Used by units in proved state: byte,
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 9
Proof steps: 22
Used lemmas: and-onel-01, and-zero-02, and-oner-01, and-zero-03, and-rec-04, and-rec-03, and-rec-02, and-rec-01, and-rec,
Used spec theorems:
- Used simplifier rules:
  - list/bitlista/e
  - list-data/bitlista/elim-list-c
  - list/bitlista/c-03
  - list/bitlista/e-01
  - list/bitlista/c-04
  - list/bitlista/app
  - list/bitlista/c
  - list-data/bitlista/lf-01
  - nat-basic1/one
  - list/bitlista/Last
  - list-last/bitlista/b-01
  - list/bitlista/app-06
  - list/bitlista/a
  - list-last/bitlista/lb
  - nat/lels-01
  - nat-basic1/one-01
  - list-data/bitlista/l
  - nat/ls-01
  - nat-basic2/s
  - nat-basic1/ref-1
  - nat-basic2/a
  - nat-basic2/c