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Proof step 20 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, err = ESUCCESS, err = err0, avol[m6 + m8].mapped?, m6 + m8 < # avol, m8 < # lpt, 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-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, m7 ≥ # avol[m6 + m8].data, logoff ≠ LEB_SIZE → # buf3 = logoff, ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ ⟨avol1 := subarray(avol0, m6, # lpt); apersistence_io_write#(m8, m7, n2, n, buf, adr, m1, log, lpt, orphans; avol1; err1)⟩ ( # avol[m6 + m8, mapped(avol[m6 + m8].data + mkempbuf(m7 - # avol[m6 + m8].data) + subarray(buf, n2, n))] = m6 + (# avol[m6 + m8, mapped(avol[m6 + m8].data + mkempbuf(m7 - # avol[m6 + m8].data) + subarray(buf, n2, n))] - m6) ∧ avol1 = subarray (avol[m6 + m8, mapped(avol[m6 + m8].data + mkempbuf(m7 - # avol[m6 + m8].data) + subarray(buf, n2, n))], m6, # avol[m6 + m8, mapped(avol[m6 + m8].data + mkempbuf(m7 - # avol[m6 + m8].data) + subarray(buf, n2, n))] - m6) ∧ is-encoded(log, avol[m6 + m8, mapped(avol[m6 + m8].data + mkempbuf(m7 - # avol[m6 + m8].data) + subarray(buf, n2, n))][m2].data) ∧ is-encoded (lpt, lebs (avol[m6 + m8, mapped(avol[m6 + m8].data + mkempbuf(m7 - # avol[m6 + m8].data) + subarray(buf, n2, n))], m5, lptlebs(# avol[m6 + m8, mapped(avol[m6 + m8].data + mkempbuf(m7 - # avol[m6 + m8].data) + subarray(buf, n2, n))] - m6, LEB_SIZE))) ∧ is-encoded-pad (orphans, m4, avol[m6 + m8, mapped(avol[m6 + m8].data + mkempbuf(m7 - # avol[m6 + m8].data) + subarray(buf, n2, n))][m3].data) ∧ err = err1), n = 0

Heuristic symbolic execution applied rule assign right

And obtained the following new goals

Proof step 21:
# avol0 = # lpt + m6, avol0[m6 + m8] = mapped(buf0), avol0[0] = mapped(buf1), avol0[m3] = mapped(buf2), avol0[m2] = mapped(buf3), avol = avol0, avol1 = subarray(avol0, m6, # lpt), err = err0, err = ESUCCESS, avol[m6 + m8].mapped?, m8 < # lpt, m6 + m8 < # avol, disk-layout(mksb(adr, m1, m2, m3, m4, m5, m6), # lpt), ebm-vol-inv(subarray(avol0, m6, # lpt)), ebm-vol-inv(avol0), 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)), m7 + n ≤ LEB_SIZE, m6 ≤ # avol0, # buf0 ≤ m7, n2 + n ≤ # buf, m6 + # lpt ≤ # avol0, m7 ≥ # avol[m6 + m8].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[m6 + m8, mapped(avol[m6 + m8].data + mkempbuf(m7 - # avol[m6 + m8].data) + subarray(buf, n2, n))] = m6 + (# avol[m6 + m8, mapped(avol[m6 + m8].data + mkempbuf(m7 - # avol[m6 + m8].data) + subarray(buf, n2, n))] - m6) ∧ avol1 = subarray (avol[m6 + m8, mapped(avol[m6 + m8].data + mkempbuf(m7 - # avol[m6 + m8].data) + subarray(buf, n2, n))], m6, # avol[m6 + m8, mapped(avol[m6 + m8].data + mkempbuf(m7 - # avol[m6 + m8].data) + subarray(buf, n2, n))] - m6) ∧ is-encoded(log, avol[m6 + m8, mapped(avol[m6 + m8].data + mkempbuf(m7 - # avol[m6 + m8].data) + subarray(buf, n2, n))][m2].data) ∧ is-encoded (lpt, lebs (avol[m6 + m8, mapped(avol[m6 + m8].data + mkempbuf(m7 - # avol[m6 + m8].data) + subarray(buf, n2, n))], m5, lptlebs(# avol[m6 + m8, mapped(avol[m6 + m8].data + mkempbuf(m7 - # avol[m6 + m8].data) + subarray(buf, n2, n))] - m6, LEB_SIZE))) ∧ is-encoded-pad (orphans, m4, avol[m6 + m8, mapped(avol[m6 + m8].data + mkempbuf(m7 - # avol[m6 + m8].data) + subarray(buf, n2, n))][m3].data) ∧ err = err1), n = 0

Rule argument

Additional information

Used simplifier rules: ⊦ n ≥ m ↔ m ≤ n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m = m0 + n0 ∧ n < n0 → m0 + n < m; (s)% ⊦ aleb.mapped? ↔ (∃ buf. aleb = mapped(buf)); (as)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ ¬ ⌊ESUCCESS⌋ ; (s)%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat% ⊦ mapped(buf) = mapped(buf0) ↔ buf = buf0; (s)% ⊦ m < n → ¬ n < m; (s)