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Proof step 92 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), avol = subarray(avol0, m6, # lpt), err = err1, m0 = n4 + # avol0[m6 + m8].data, m1 = m8, n1 = n0, avol0[m6 + m8].mapped?, m6 + m8 < # avol0, 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)), m6 + # lpt ≤ # avol0, n4 + # buf0 + n ≤ LEB_SIZE, n0 + n3 ≤ # buf, n0 + n ≤ # buf, ⌊err1⌋ , logoff ≠ LEB_SIZE → # buf3 = logoff ⊦ (∀ n2. ¬(n2 < n ∧ is-aligned(n2, EB_PAGE_SIZE))) ∧ ⟨skip⟩ ( avol = subarray(avol0, m6, # lpt)[m8, mapped(avol0[m6 + m8].data + mkempbuf(n4) + subarray(buf, n0, n3))] ∧ is-encoded(log, avol0[m6 + m8, mapped(avol0[m6 + m8].data + mkempbuf(n4) + subarray(buf, n0, n3))][m2].data) ∧ is-encoded-pad(orphans, m4, avol0[m3].data) ∧ err1 = err), ∃ n2. (n2 < n ∧ is-aligned(n2, EB_PAGE_SIZE)) ∧ ⟨if n2 ≠ 0 then avol[m1] := mapped(avol[m1].data + mkempbuf(m0 - # avol[m1].data) + subarray(buf, n1, n2))⟩ ( avol = subarray(avol0, m6, # lpt)[m8, mapped(avol0[m6 + m8].data + mkempbuf(n4) + subarray(buf, n0, n3))] ∧ is-encoded(log, avol0[m6 + m8, mapped(avol0[m6 + m8].data + mkempbuf(n4) + subarray(buf, n0, n3))][m2].data) ∧ is-encoded-pad(orphans, m4, avol0[m3].data) ∧ err1 = err), n3 = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 93:
# avol0 = # lpt + m6, avol0[m6 + m8] = mapped(buf0), avol0[m2] = mapped(buf3), avol0[m3] = mapped(buf2), avol0[0] = mapped(buf1), avol = subarray(avol0, m6, # lpt), n3 ≠ 0, 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)), n0 + n ≤ # buf, n0 + n3 ≤ # buf, n4 + # buf0 + n ≤ LEB_SIZE, ⌊err1⌋ , logoff ≠ LEB_SIZE → # buf3 = logoff ⊦ (¬ n1 < n ∨ ¬ is-aligned(n1, EB_PAGE_SIZE)) ∧ ⟨skip⟩ ( subarray(avol0, m6, # lpt) = subarray(avol0, m6, # lpt)[m8, mapped(avol0[m6 + m8].data + mkempbuf(n4) + subarray(buf, n0, n3))] ∧ is-encoded(log, avol0[m6 + m8, mapped(avol0[m6 + m8].data + mkempbuf(n4) + subarray(buf, n0, n3))][m2].data) ∧ is-encoded-pad(orphans, m4, avol0[m3].data)), ∃ n2. n2 < n ∧ is-aligned(n2, EB_PAGE_SIZE) ∧ ⟨if n2 ≠ 0 then avol[m8] := mapped(avol[m8].data + mkempbuf(n4 + # avol0[m6 + m8].data - # avol[m8].data) + subarray(buf, n0, n2))⟩ ( avol = subarray(avol0, m6, # lpt)[m8, mapped(avol0[m6 + m8].data + mkempbuf(n4) + subarray(buf, n0, n3))] ∧ is-encoded(log, avol0[m6 + m8, mapped(avol0[m6 + m8].data + mkempbuf(n4) + subarray(buf, n0, n3))][m2].data) ∧ is-encoded-pad(orphans, m4, avol0[m3].data))

Rule argument

Additional information

Used simplifier rules: ⊦ m ≤ m; (s)% ⊦ mapped(buf) = mapped(buf0) ↔ buf = buf0; (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