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Theorem and-notempty

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

Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by: and-ass, and-notempty-01, and-notempty-02, and-notempty-03, and-notempty-04, and-notempty-05, and-notempty-07, and-notempty-08, and-notempty-09, and-sgn, band-011x-neg, band-011x-pos, band-associativity, bitsand-app-zeros, bitsand-cast, bitsand-fillsgn, bitsxor-is-orand, bor-2pot-plus, bor-2pot-plus-01, bor-notAndNot, bxor-def-logic, cast-law-and-one,
Used by units in proved state: byte,
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 6
Proof steps: 16
Used lemmas: and-rec-04, and-rec-03, and-rec-02, and-rec-01, and-rec,
Used spec theorems:
- Used simplifier rules:
  - list/bitlista/c-04
  - list/bitlista/c-03
  - list/bitlista/e-01
  - list-data/bitlista/elim-list-c
  - list/bitlista/app
  - list/bitlista/c
  - list-data/bitlista/lf-01
  - list-data/bitlista/l
  - nat-basic1/one
  - list/bitlista/Last
  - list/bitlista/app-02-ant
  - list/bitlista/e
  - list/bitlista/a