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Proof step 151 from proof refine-write (previous step)

# avol0 = # lpt + m6, avol0[m6 + m8] = mapped(buf0), avol0[m2] = mapped(buf3), avol0[m3] = mapped(buf2), avol0[0] = mapped(buf1), avol = avol0, avol1 = subarray(avol0, m6, # lpt), m = m7, m0 = m8, sb = mksb(adr, m1, m2, m3, m4, m5, m6), 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, m7 + n ≤ LEB_SIZE, # buf0 ≤ m7, m6 ≤ # avol0, logoff ≠ LEB_SIZE → # buf3 = logoff, sb.main + m0 < # avol → sb.main + m0 < # avol ∧ (avol[sb.main + m0].mapped? → avol[sb.main + m0].mapped? ∧ sb.main + m0 < # avol) ⊦ sb.main + m0 < # avol ∧ avol[sb.main + m0].mapped? ∧ # avol[sb.main + m0].data ≤ m ∧ is-aligned(m, EB_PAGE_SIZE) ∧ is-aligned(n, EB_PAGE_SIZE) ∧ m + n ≤ LEB_SIZE ∧ n0 + n ≤ # buf

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

Additional information

Used simplifier rules: ⊦ mapped(buf).data = buf; (s)% ⊦ mapped(buf).mapped?; (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% ⊦ mksb(adr, m, m0, m1, m2, m3, m4).main = m4; (s)