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Theorem and-rec

⊦ 1 < # bits ∧ 1 < # bits0 → bitsand(bits, bits0) = bitsand(bits.butlast, bits0.butlast) + (bits.last ∧ bits0.last)

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by: add-ones-grlen, add-ones-grlen-02, add-ones-lelen, and-011x-neg, and-ass, and-com, and-false, and-first, and-insgn, and-notempty, and-notone-01, and-ones, and-onesin, and-rec-06, and-rec-07, and-rec-08, and-rec-09, and-sgn, and-size-one, and-size-one-01, and-true, and-two, and-zerosin, band-011x-pos, band-max, band-min, bitsand-app, bitsand-app-false, bitsand-app-ones, bitsand-app-true, bitsand-app-zeros, bitsand-app-zeros-01, bitsand-fillsgn, bitsand-first-samesize, bitsand-idempotent, bitsand-len-false, bitsand-len-true, bitsand-onein, bitsand-zero-in, bitsand-zeros, bitsand-zeros-01, bitsxor-is-orand, or-invandinv,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 4
Proof steps: 7
Used lemmas: bitsand-rec,
Used spec theorems:
- list/bitlista/lastdiv
Used simplifier rules:
- list/bitlista/app-01
- list/bitlista/in-17
- list/bitlista/in-append
- list/bitlista/in-15
- list/bitlista/first-01
- list/bitlista/c-04
- list/bitlista/first
- list/bitlista/Nil
- list/bitlista/e-02
- list/bitlista/a
- list/bitlista/app
- list/bitlista/c
- list-data/bitlista/lf-01
- list-data/bitlista/l
- nat-basic1/one
- list/bitlista/Last
- list-last/bitlista/last-elim