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Proof step 28 from proof refine-write (previous step)

# avol0 = # lpt + m6, avol0[0] = mapped(buf1), avol0[m3] = mapped(buf2), avol0[m2] = mapped(buf3), avol0[m6 + m8] = mapped(buf0), avol = avol1, avol1 = subarray(avol0, m6, # lpt), m = m7, m0 = n3 + # avol0[m6 + m8].data, m1 = m8, n0 = n, n1 = n2, ns = orphans, plog = log, avol[m1].mapped?, avol0[m6 + m8].mapped?, m1 < # avol, m8 < # lpt, m6 + m8 < # avol0, disk-layout(mksb(adr, m7, m2, m3, m4, m5, m6), # lpt), ebm-vol-inv(subarray(avol0, m6, # lpt)), ebm-vol-inv(avol0), is-aligned(m0, EB_PAGE_SIZE), is-aligned(n0, EB_PAGE_SIZE), 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)), # avol[m1].data ≤ m0, m0 + n0 ≤ LEB_SIZE, n1 + n0 ≤ # buf, n2 + n ≤ # buf, n3 + # buf0 + n ≤ LEB_SIZE, m1 < # avol → m1 < # avol ∧ (avol[m1].mapped? → avol[m1].mapped? ∧ m1 < # avol), logoff ≠ LEB_SIZE → # buf3 = logoff ⊦ ⟨fail_or_success#(; ; err); if err = ESUCCESS then if n0 ≠ 0 then avol[m1] := mapped(avol[m1].data + mkempbuf(m0 - # avol[m1].data) + subarray(buf, n1, n0)) else choose n with n < n0 ∧ is-aligned(n, EB_PAGE_SIZE) in if n ≠ 0 then avol[m1] := mapped(avol[m1].data + mkempbuf(m0 - # avol[m1].data) + subarray(buf, n1, n)) ifnone skip⟩ ( avol = 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), n = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 29:
# avol0 = # lpt + m6, avol0[m2] = mapped(buf3), avol0[m3] = mapped(buf2), avol0[0] = mapped(buf1), avol0[m6 + m8] = mapped(buf0), n ≠ 0, 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)), n3 + # buf0 + n ≤ LEB_SIZE, n2 + n ≤ # buf, logoff ≠ LEB_SIZE → # buf3 = logoff ⊦ ⟨fail_or_success#(; ; err); avol := subarray(avol0, m6, # lpt); if err = ESUCCESS then if n ≠ 0 then avol[m8] := mapped(avol[m8].data + mkempbuf(n3 + # avol0[m6 + m8].data - # avol[m8].data) + subarray(buf, n2, n)) else {n1 := n2; n0 := n; m1 := m8; m0 := n3 + # avol0[m6 + m8].data; choose n4 with n4 < n0 ∧ is-aligned(n4, EB_PAGE_SIZE) in if n4 ≠ 0 then avol[m1] := mapped(avol[m1].data + mkempbuf(m0 - # avol[m1].data) + subarray(buf, n1, n4)) ifnone skip}⟩ ( avol = 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)

Rule argument

Additional information

Used simplifier rules: ⊦ mapped(buf).data = buf; (s)% ⊦ mapped(buf) = mapped(buf0) ↔ buf = buf0; (s)% ⊦ aleb.mapped? ↔ (∃ buf. aleb = mapped(buf)); (as)% ⊦ # subarray(avol, m, n) = n; (s)% ⊦ 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% ⊦ m ≤ m + n; (s)% ⊦ n0 < n → subarray(avol, m, n)[n0] = avol[m + n0]; (s)