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Proof step 9 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 = avol0, avol1 = subarray(avol0, m6, # lpt), m = m7, m0 = m8, sb = mksb(adr, m1, m2, m3, m4, m5, m6), avol[sb.main + m0].mapped?, sb.main + m0 < # avol, 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(m, 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)), # avol[sb.main + m0].data ≤ m, m + n ≤ LEB_SIZE, m6 ≤ # avol0, # buf0 ≤ m7, m7 + n ≤ LEB_SIZE, n0 + n ≤ # buf, sb.main + m0 < # avol → sb.main + m0 < # avol ∧ (avol[sb.main + m0].mapped? → avol[sb.main + m0].mapped? ∧ sb.main + m0 < # avol), logoff ≠ LEB_SIZE → # buf3 = logoff ⊦ ⟪ebm_avol_write#(sb.main + m0, m, n0, n, buf; avol; err)⟫ ⟨apersistence_io_write#(m8, m7, n0, n, buf, adr, m1, log, lpt, orphans; avol1; err0)⟩ ( # avol = m6 + (# avol - m6) ∧ avol1 = subarray(avol, m6, # avol - m6) ∧ is-encoded(log, avol[m2].data) ∧ is-encoded(lpt, lebs(avol, m5, lptlebs(# avol - m6, LEB_SIZE))) ∧ is-encoded-pad(orphans, m4, avol[m3].data) ∧ err = err0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
# avol0 = # lpt + m6, avol0[m2] = mapped(buf3), avol0[m3] = mapped(buf2), avol0[0] = mapped(buf1), avol0[m6 + m8] = mapped(buf0), avol = avol0, 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)), n0 + n ≤ # buf, # buf0 ≤ m7, m6 ≤ # avol0, m7 + n ≤ LEB_SIZE, logoff ≠ LEB_SIZE → # buf3 = logoff ⊦ ⟪ebm_avol_write#(m6 + m8, m7, n0, n, buf; avol; err)⟫ ⟨avol1 := subarray(avol0, m6, # lpt); apersistence_io_write#(m8, m7, n0, n, buf, adr, m1, log, lpt, orphans; avol1; err0)⟩ ( # avol = m6 + (# avol - m6) ∧ avol1 = subarray(avol, m6, # avol - m6) ∧ is-encoded(log, avol[m2].data) ∧ is-encoded(lpt, lebs(avol, m5, lptlebs(# avol - m6, LEB_SIZE))) ∧ is-encoded-pad(orphans, m4, avol[m3].data) ∧ err = err0)

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)% ⊦ 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% ⊦ mksb(adr, m, m0, m1, m2, m3, m4).main = m4; (s)