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Proof step 72 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 = avol0, avol1 = subarray(avol0, m6, # lpt), err = err0, m = m7, m0 = m6 + m8, n0 = n, n1 = n2, avol[m0].mapped?, m8 < # lpt, n3 < n0, m0 < # avol, disk-layout(mksb(adr, m1, 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(m7, EB_PAGE_SIZE), is-aligned(n3, EB_PAGE_SIZE), is-encoded(log, buf3), is-encoded(lpt, lebs(avol0, m5, lptlebs(# lpt, LEB_SIZE))), is-encoded(mksb(adr, m1, m2, m3, m4, m5, m6), buf1), is-encoded-pad(orphans, m4, buf2), mapped-full?(avol0, m5, lptlebs(# lpt, LEB_SIZE)), n2 + n ≤ # buf, # buf0 ≤ m7, m6 ≤ # avol0, m7 + n ≤ LEB_SIZE, n1 + n3 ≤ # buf, m6 + # lpt ≤ # avol0, m ≥ # avol[m0].data, logoff ≠ LEB_SIZE → # buf3 = logoff, ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ ⟨apersistence_io_write#(m8, m7, n2, n, buf, adr, m1, log, lpt, orphans; avol1; err1)⟩ ( # avol[m0, mapped(avol[m0].data + mkempbuf(m - # avol[m0].data) + subarray(buf, n1, n3))] = m6 + (# avol[m0, mapped(avol[m0].data + mkempbuf(m - # avol[m0].data) + subarray(buf, n1, n3))] - m6) ∧ avol1 = subarray (avol[m0, mapped(avol[m0].data + mkempbuf(m - # avol[m0].data) + subarray(buf, n1, n3))], m6, # avol[m0, mapped(avol[m0].data + mkempbuf(m - # avol[m0].data) + subarray(buf, n1, n3))] - m6) ∧ is-encoded(log, avol[m0, mapped(avol[m0].data + mkempbuf(m - # avol[m0].data) + subarray(buf, n1, n3))][m2].data) ∧ is-encoded (lpt, lebs (avol[m0, mapped(avol[m0].data + mkempbuf(m - # avol[m0].data) + subarray(buf, n1, n3))], m5, lptlebs(# avol[m0, mapped(avol[m0].data + mkempbuf(m - # avol[m0].data) + subarray(buf, n1, n3))] - m6, LEB_SIZE))) ∧ is-encoded-pad(orphans, m4, avol[m0, mapped(avol[m0].data + mkempbuf(m - # avol[m0].data) + subarray(buf, n1, n3))][m3].data) ∧ err = err1), err = ESUCCESS, n3 = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 73:
# avol0 = # lpt + m6, avol0[0] = mapped(buf1), avol0[m3] = mapped(buf2), avol0[m2] = mapped(buf3), avol0[m6 + m8] = mapped(buf0), avol1 = subarray(avol0, m6, # lpt), n3 ≠ 0, n3 < n, m8 < # lpt, disk-layout(mksb(adr, m1, m2, m3, m4, m5, m6), # lpt), ebm-vol-inv(subarray(avol0, m6, # lpt)), ebm-vol-inv(avol0), is-aligned(n3, EB_PAGE_SIZE), is-aligned(m7, EB_PAGE_SIZE), is-aligned(n, EB_PAGE_SIZE), is-encoded(mksb(adr, m1, 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 + n3 ≤ # buf, m7 + n ≤ LEB_SIZE, # buf0 ≤ m7, n2 + n ≤ # buf, m6 ≤ # avol0, ⌊err0⌋ , logoff ≠ LEB_SIZE → # buf3 = logoff ⊦ ⟨apersistence_io_write#(m8, m7, n2, n, buf, adr, m1, log, lpt, orphans; avol1; err1)⟩ ( avol1 = subarray (avol0[m6 + m8, mapped(avol0[m6 + m8].data + mkempbuf(m7 - # avol0[m6 + m8].data) + subarray(buf, n2, n3))], m6, # avol0 - m6) ∧ is-encoded(log, avol0[m6 + m8, mapped(avol0[m6 + m8].data + mkempbuf(m7 - # avol0[m6 + m8].data) + subarray(buf, n2, n3))][m2].data) ∧ is-encoded (lpt, lebs (avol0[m6 + m8, mapped(avol0[m6 + m8].data + mkempbuf(m7 - # avol0[m6 + m8].data) + subarray(buf, n2, n3))], m5, lptlebs(# avol0 - m6, LEB_SIZE))) ∧ is-encoded-pad(orphans, m4, avol0[m3].data) ∧ err0 = err1)

Rule argument

Additional information

Used simplifier rules: ⊦ mapped(buf).data = buf; (s)% ⊦ m ≤ m; (s)% ⊦ m < n → n ≠ 0; (s)% ⊦ mapped(buf) = mapped(buf0) ↔ buf = buf0; (s)%let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%m ≠ n ⊦ avol[m, aleb][n] = avol[n]; (s)%⊦ disk-layout(mksb(adr, m0, m1, m2, m, m3, m4), mainareasize) → m4 + n ≠ m2; (s)%n ≤ m ⊦ (m - n) + n0 = n1 ↔ m + n0 = n + n1; (s)% ⊦ m ≤ n → (n < m ↔ false); (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ # avol[n, aleb] = # avol; (s)% ⊦ ⌊err⌋ → err ≠ ESUCCESS; (s)% ⊦ aleb.mapped? ↔ (∃ buf. aleb = mapped(buf)); (as)% ⊦ m = m0 + n0 ∧ n < n0 → m0 + n < m; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ n ≥ m ↔ m ≤ n; (s)