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Proof step 24 from proof valid-wl-use (previous step)

# apebs = # wlar, apebs[n] = mkpeb(aehdr1, avhdr1, buf1, m2, boolvar1), n < # wlar, valid-peb(v, m, mkpeb(aehdr0, avhdr0, buf0, m1, false)), valid-sqns(v, m, apebs) ≠ ∅ → valid-sqns(v, m, apebs).max < avhdr0.sqn, ∀ n. n < # wlar → (wlar[n].status = erroneous ↔ apebs[n].bad) ∧ (wlar[n].status = free → apebs[n].vidhdr = empty) ∧ (wlar[n].status ≠ erroneous ∧ wlar[n].status ≠ erasing → apebs[n].echdr = aechdr(wlar[n].ec)) ∧ (wlar[n].status = used → (∃ v, m. valid-peb(v, m, apebs[n]) ∧ apebs[n].vidhdr.sqn = valid-sqns(v, m, apebs).max)), ∀ m0. m0 < # wlar ∧ m0 ≠ n ∧ wlar[m0].status = used → apebs[m0].vidhdr.vol ≠ v ∨ apebs[m0].vidhdr.leb ≠ m ⊦ aehdr0 = aechdr(aehdr0.ec)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 25:
⊦ valid-peb(v, m, apeb) ↔ ¬ apeb.bad ∧ apeb.echdr.valid? ∧ (∃ m0, m1, m2. apeb.vidhdr = avidhdr(v, m, m0, m1, m2) ∧ (m1 ≠ 0 → m1 ≤ datasize(apeb.data) ∧ m2 = checksum(apeb.data, m1)))
Proof step 26:
# apebs = # wlar, apebs[n] = mkpeb(aehdr1, avhdr1, buf1, m2, boolvar1), mkpeb(aehdr0, avhdr0, buf0, m1, false).echdr.valid?, n < # wlar, valid-sqns(v, m, apebs) ≠ ∅ → valid-sqns(v, m, apebs).max < avhdr0.sqn, ∀ m0. m0 < # wlar ∧ m0 ≠ n ∧ wlar[m0].status = used → apebs[m0].vidhdr.vol ≠ v ∨ apebs[m0].vidhdr.leb ≠ m, ∀ n. n < # wlar → (wlar[n].status = erroneous ↔ apebs[n].bad) ∧ (wlar[n].status = free → apebs[n].vidhdr = empty) ∧ (wlar[n].status ≠ erroneous ∧ wlar[n].status ≠ erasing → apebs[n].echdr = aechdr(wlar[n].ec)) ∧ (wlar[n].status = used → (∃ v, m. valid-peb(v, m, apebs[n]) ∧ apebs[n].vidhdr.sqn = valid-sqns(v, m, apebs).max)), ∃ m0, m3, m2. mkpeb(aehdr0, avhdr0, buf0, m1, false).vidhdr = avidhdr(v, m, m0, m3, m2) ∧ (m3 ≠ 0 → m3 ≤ datasize(mkpeb(aehdr0, avhdr0, buf0, m1, false).data) ∧ m2 = checksum(mkpeb(aehdr0, avhdr0, buf0, m1, false).data, m3)) ⊦ aehdr0 = aechdr(aehdr0.ec), mkpeb(aehdr0, avhdr0, buf0, m1, false).bad

Rule argument

spec: valid-peb name: valid-peb2 seq: ⊦ valid-peb(v, m, apeb) ↔ ¬ apeb.bad ∧ apeb.echdr.valid? ∧ (∃ m0, m1, m2. apeb.vidhdr = avidhdr(v, m, m0, m1, m2) ∧ ( m1 ≠ 0 → m1 ≤ datasize(apeb.data) ∧ m2 = checksum(apeb.data, m1))) subst: [apeb, m, v] → [mkpeb(aehdr0, avhdr0, buf0, m1, false), m, v] flags: <all paths>

Additional information

Used terms: mkpeb(aehdr0, avhdr0, buf0, m1, false), m, v