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Theorem and-rec-02

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

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by: add-ones-grlen-02, and-ass, and-com, and-first, and-insgn, and-notempty, and-one, and-onesin, and-sgn, and-true, and-zero-03, and-zerosin, band-011x-pos, band-max, bitsand-app-false, bitsand-app-ones, bitsand-app-zeros, bitsand-app-zeros-01, bitsand-false-01, bitsand-fillsgn, bitsand-onein, bitsand-zero-in, bitsxor-is-orand, cast-band, or-invandinv,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 1
Proof steps: 2
Used lemmas: bitsand-zeror,
Used spec theorems:
- list/bitlista/lastdiv-rew
Used simplifier rules:
- list/bitlista/a
- list/bitlista/c-04