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Theorem band-associativity

⊦ band(i, band(i0, j)) = band(band(i, i0), j)

Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by: band-011x-eq, band-011x-is-unsigned, band-011x-is-unsigned-03, band-011x-is-unsigned-fix, band-011x-is-unsigned-fix-01, band-011x-neg, band-011x-neg-01, band-011x-neg-02, band-011x-pos, band-011x-pos-01, band-011x-pos-02, band-011x-zero, band-255-neg, band-255-pos, band-32-not-neg, band-63-lezero, band-65535-neg, band-65535-pos, band-commutativity, band-idempotent, band-le-zero, band-ls-zero-01, band-max-01, band-max-02, band-max-03, band-max-04, band-max-05, band-max-06, band-mod256-neg, band-mod256-pos, band-notneg, band-num, bor-assoc, bor-notAndNot, bor-zero, bxor-minus-one, bxor-zero, divide-by-10, intshiftleft-band31, intshiftright-ls-02, intshiftright-mone, intshiftright-unbounded-same, intshiftrsign-abs-le, intshiftrsign-rec-neg, intshiftrsign-rec-pos, intshiftrsign-zero, intshiftrsign-zero-01, intshiftrsign32, intshiftrzero-prop-01, intshiftzero-mone, longshiftright-2pot-pos, longshiftzero-band-63, longshiftzero-carry, longshiftzero-carry-01, longshiftzero-zero-02, longshiftzero-zero-03,
Used by units in proved state: bytes, byte,
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 9
Proof steps: 18
Used lemmas: and-ass, and-com, and-sgn, and-notempty, and-notempty-09, band-def,
Used spec theorems:
- int2bits/bits2int-inj
Used simplifier rules: