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Proof step 39 from proof refine-write (previous step)

# avol0 = # lpt + m6, avol0[m2] = mapped(buf3), avol0[m3] = mapped(buf2), avol0[0] = mapped(buf1), avol0[m6 + m8] = mapped(buf0), avol = subarray(avol0, m6, # lpt), err = ESUCCESS, avol0[m6 + m8].mapped?, avol[m8].mapped?, m6 + m8 < # avol0, m8 < # avol, m8 < # lpt, disk-layout(mksb(adr, m7, m2, m3, m4, m5, m6), # lpt), ebm-vol-inv(avol0), ebm-vol-inv(subarray(avol0, m6, # lpt)), is-aligned(n, EB_PAGE_SIZE), is-aligned(n3 + # buf0, EB_PAGE_SIZE), is-encoded(log, buf3), is-encoded(lpt, lebs(avol0, m5, lptlebs(# lpt, LEB_SIZE))), is-encoded(mksb(adr, m7, m2, m3, m4, m5, m6), buf1), is-encoded-pad(orphans, m4, buf2), mapped-full?(avol0, m5, lptlebs(# lpt, LEB_SIZE)), m6 + # lpt ≤ # avol0, n3 + # buf0 + n ≤ LEB_SIZE, n2 + n ≤ # buf, n3 + # avol0[m6 + m8].data ≥ # avol[m8].data, logoff ≠ LEB_SIZE → # buf3 = logoff ⊦ n = 0, avol[m8, mapped(avol[m8].data + mkempbuf(n3 + # avol0[m6 + m8].data - # avol[m8].data) + subarray(buf, n2, n))] = subarray(avol0, m6, # lpt)[m8, mapped(avol0[m6 + m8].data + mkempbuf(n3) + subarray(buf, n2, n))] ∧ is-encoded(log, avol0[m6 + m8, mapped(avol0[m6 + m8].data + mkempbuf(n3) + subarray(buf, n2, n))][m2].data) ∧ is-encoded-pad(orphans, m4, avol0[m3].data) ∧ ESUCCESS = err

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 40:
# avol0 = # lpt + m6, avol0[0] = mapped(buf1), avol0[m3] = mapped(buf2), avol0[m2] = mapped(buf3), avol0[m6 + m8] = mapped(buf0), m8 < # lpt, disk-layout(mksb(adr, m7, m2, m3, m4, m5, m6), # lpt), ebm-vol-inv(subarray(avol0, m6, # lpt)), ebm-vol-inv(avol0), is-aligned(n3 + # buf0, EB_PAGE_SIZE), is-aligned(n, EB_PAGE_SIZE), is-encoded(mksb(adr, m7, m2, m3, m4, m5, m6), buf1), is-encoded(lpt, lebs(avol0, m5, lptlebs(# lpt, LEB_SIZE))), is-encoded(log, buf3), is-encoded-pad(orphans, m4, buf2), mapped-full?(avol0, m5, lptlebs(# lpt, LEB_SIZE)), n2 + n ≤ # buf, n3 + # buf0 + n ≤ LEB_SIZE, logoff ≠ LEB_SIZE → # buf3 = logoff ⊦ n = 0, is-encoded(log, avol0[m6 + m8, mapped(buf0 + mkempbuf(n3) + subarray(buf, n2, n))][m2].data)

Rule argument

Additional information

Used simplifier rules: ⊦ is-encoded-pad(ns0, n, buf) → (is-encoded-pad(ns1, n, buf) ↔ ns0 = ns1); (s)% ⊦ mapped(buf).data = buf; (s)% ⊦ m ≤ m; (s)% ⊦ mapped(buf) = mapped(buf0) ↔ buf = buf0; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ m + n - m = n; (s)% ⊦ aleb.mapped? ↔ (∃ buf. aleb = mapped(buf)); (as)% ⊦ m = m0 + n0 ∧ n < n0 → m0 + n < m; (s)% ⊦ # subarray(avol, m, n) = n; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m ≤ m + n; (s)% ⊦ n ≥ m ↔ m ≤ n; (s)% ⊦ n0 < n → subarray(avol, m, n)[n0] = avol[m + n0]; (s)