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Proof step 90 from proof vols-is-max-is-max-vols (previous step)

# vols0[v] = # vols1[v], # apebs = # wlar1, # wlar0 = # wlar1, avhdr.leb = VTBL_LNUM, avhdr.vol = VTBL_VOLID, wlar0[m0] = wl-entry(m3, used), apebs[m0] = mkpeb(aehdr, avhdr, buf, m2, boolvar), wlar1[m0] = wl-entry(m4, used), apebs[m5] = mkpeb(aechdr(m10), avidhdr(v, m, valid-sqns(v0, m11, apebs).max, m7, m8), buf0, m9, false), wlar1[m5] = wl-entry(m10, used), apebs[m6] = mkpeb(aechdr(m16), avidhdr(v, m, valid-sqns(v1, m17, apebs).max, m13, m14), buf1, m15, false), wlar0[m6] = wl-entry(m16, used), ⌜m5⌝ = vols1[v][m], ⌜m6⌝ = vols0[v][m], m0 < # wlar1, m5 < # wlar1, m < # vols1[v], m6 < # wlar1, bflipset-cons(bflipset0, wlar0), bflipset-cons(bflipset1, wlar1), is-encoded(to-vtbl(vols1), buf), unique-elems(valid-sqns(v, m, apebs)), valid-eraseq(apebs, q0), valid-eraseq(wlar0, q0), valid-eraseq(q0), valid-eraseq(apebs, q1), valid-eraseq(wlar1, q1), valid-eraseq(q1), valid-eraseq-strong(apebs, to-vtbl(vols1), q0), valid-global-sqn(apebs, n1), valid-global-sqn(apebs, m1), valid-peb(v1, m17, mkpeb(aechdr(m16), avidhdr(v, m, valid-sqns(v1, m17, apebs).max, m13, m14), buf1, m15, false)), valid-peb(v0, m11, mkpeb(aechdr(m10), avidhdr(v, m, valid-sqns(v0, m11, apebs).max, m7, m8), buf0, m9, false)), v ∈ vols0, v ∈ vols1 ⊦ m5 = m0, m5 = m6, m6 = m0, VTBL_VOLID ∈ vols0, VTBL_VOLID ∈ vols1, v1 = v ∧ m17 = m ∧ v0 = v ∧ m11 = m

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 91:
⊦ 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 92:
# wlar0 = # wlar1, # apebs = # wlar1, # vols0[v] = # vols1[v], avhdr.leb = VTBL_LNUM, avhdr.vol = VTBL_VOLID, wlar0[m6] = wl-entry(m16, used), apebs[m6] = mkpeb(aechdr(m16), avidhdr(v, m, valid-sqns(v1, m17, apebs).max, m13, m14), buf1, m15, false), wlar1[m5] = wl-entry(m10, used), apebs[m5] = mkpeb(aechdr(m10), avidhdr(v, m, valid-sqns(v0, m11, apebs).max, m7, m8), buf0, m9, false), wlar1[m0] = wl-entry(m4, used), apebs[m0] = mkpeb(aehdr, avhdr, buf, m2, boolvar), wlar0[m0] = wl-entry(m3, used), ⌜m6⌝ = vols0[v][m], ⌜m5⌝ = vols1[v][m], mkpeb(aechdr(m10), avidhdr(v, m, valid-sqns(v0, m11, apebs).max, m7, m8), buf0, m9, false).echdr.valid?, m6 < # wlar1, m < # vols1[v], m5 < # wlar1, m0 < # wlar1, bflipset-cons(bflipset1, wlar1), bflipset-cons(bflipset0, wlar0), is-encoded(to-vtbl(vols1), buf), unique-elems(valid-sqns(v, m, apebs)), valid-eraseq(q1), valid-eraseq(wlar1, q1), valid-eraseq(apebs, q1), valid-eraseq(q0), valid-eraseq(wlar0, q0), valid-eraseq(apebs, q0), valid-eraseq-strong(apebs, to-vtbl(vols1), q0), valid-global-sqn(apebs, m1), valid-global-sqn(apebs, n1), valid-peb(v1, m17, mkpeb(aechdr(m16), avidhdr(v, m, valid-sqns(v1, m17, apebs).max, m13, m14), buf1, m15, false)), v ∈ vols1, v ∈ vols0, ∃ m0, m1, m2. mkpeb(aechdr(m10), avidhdr(v, m, valid-sqns(v0, m11, apebs).max, m7, m8), buf0, m9, false).vidhdr = avidhdr(v0, m11, m0, m1, m2) ∧ ( m1 ≠ 0 → m1 ≤ datasize(mkpeb(aechdr(m10), avidhdr(v, m, valid-sqns(v0, m11, apebs).max, m7, m8), buf0, m9, false).data) ∧ m2 = checksum(mkpeb(aechdr(m10), avidhdr(v, m, valid-sqns(v0, m11, apebs).max, m7, m8), buf0, m9, false).data, m1)) ⊦ m5 = m6, m5 = m0, m6 = m0, mkpeb(aechdr(m10), avidhdr(v, m, valid-sqns(v0, m11, apebs).max, m7, m8), buf0, m9, false).bad, VTBL_VOLID ∈ vols1, VTBL_VOLID ∈ vols0, v1 = v ∧ m17 = m ∧ v0 = v ∧ m11 = m

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 (aechdr(m10), avidhdr(v, m, valid-sqns(v0, m11, apebs).max, m7, m8), buf0, m9, false), m11, v0] flags: <all paths>

Additional information

Used terms: mkpeb (aechdr(m10), avidhdr(v, m, valid-sqns(v0, m11, apebs).max, m7, m8), buf0, m9, false), m11, v0