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Proof step 86 from proof refine-write (previous step)

# avol0 = # lpt + m6, avol0[m6 + m8] = mapped(buf0), avol0[0] = mapped(buf1), avol0[m3] = mapped(buf2), avol0[m2] = mapped(buf3), err = err1, n3 < n, 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, EB_PAGE_SIZE), is-aligned(n, EB_PAGE_SIZE), is-aligned(n4 + # buf0, 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)), n4 + # buf0 + n ≤ LEB_SIZE, n2 + n3 ≤ # buf, n2 + n ≤ # buf, ⌊err1⌋ , logoff ≠ LEB_SIZE → # buf3 = logoff ⊦ ⟨avol := subarray(avol0, m6, # lpt); if err = ESUCCESS then if n ≠ 0 then avol[m8] := mapped(avol[m8].data + mkempbuf(n4 + # avol0[m6 + m8].data - # avol[m8].data) + subarray(buf, n2, n)) else {n1 := n2; m1 := m8; m0 := n4 + # avol0[m6 + m8].data; choose n2 with n2 < n ∧ is-aligned(n2, EB_PAGE_SIZE) in if n2 ≠ 0 then avol[m1] := mapped(avol[m1].data + mkempbuf(m0 - # avol[m1].data) + subarray(buf, n1, n2)) ifnone skip}⟩ ( avol = subarray(avol0, m6, # lpt)[m8, mapped(avol0[m6 + m8].data + mkempbuf(n4) + subarray(buf, n2, n3))] ∧ is-encoded(log, avol0[m6 + m8, mapped(avol0[m6 + m8].data + mkempbuf(n4) + subarray(buf, n2, n3))][m2].data) ∧ is-encoded-pad(orphans, m4, avol0[m3].data) ∧ err1 = err), n3 = 0

Heuristic symbolic execution applied rule assign right

And obtained the following new goals

Proof step 87:
# 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 = err1, m8 < # lpt, n3 < n, disk-layout(mksb(adr, m7, m2, m3, m4, m5, m6), # lpt), ebm-vol-inv(avol0), ebm-vol-inv(subarray(avol0, m6, # lpt)), is-aligned(n4 + # buf0, EB_PAGE_SIZE), is-aligned(n, 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, m7, m2, m3, m4, m5, m6), buf1), is-encoded-pad(orphans, m4, buf2), mapped-full?(avol0, m5, lptlebs(# lpt, LEB_SIZE)), n2 + n ≤ # buf, n2 + n3 ≤ # buf, n4 + # buf0 + n ≤ LEB_SIZE, m6 + # lpt ≤ # avol0, ⌊err1⌋ , logoff ≠ LEB_SIZE → # buf3 = logoff ⊦ ⟨if err = ESUCCESS then if n ≠ 0 then avol[m8] := mapped(avol[m8].data + mkempbuf(n4 + # avol0[m6 + m8].data - # avol[m8].data) + subarray(buf, n2, n)) else {n1 := n2; m1 := m8; m0 := n4 + # avol0[m6 + m8].data; choose n2 with n2 < n ∧ is-aligned(n2, EB_PAGE_SIZE) in if n2 ≠ 0 then avol[m1] := mapped(avol[m1].data + mkempbuf(m0 - # avol[m1].data) + subarray(buf, n1, n2)) ifnone skip}⟩ ( avol = subarray(avol0, m6, # lpt)[m8, mapped(avol0[m6 + m8].data + mkempbuf(n4) + subarray(buf, n2, n3))] ∧ is-encoded(log, avol0[m6 + m8, mapped(avol0[m6 + m8].data + mkempbuf(n4) + subarray(buf, n2, n3))][m2].data) ∧ is-encoded-pad(orphans, m4, avol0[m3].data) ∧ err1 = err), n3 = 0

Rule argument

Additional information

Used simplifier rules: ⊦ EB_PAGE_SIZE ≠ 0; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic% ⊦ m < n → n ≠ 0; (s)% ⊦ m + n < m + n0 ↔ n < n0; (s)% ⊦ ¬ n < n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%m ≠ 0, is-aligned(n1, m) ⊦ is-aligned(n0 + n1, m) ↔ is-aligned(n0, m); (s)% ⊦ m < n → ¬ n < m; (s)