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Proof step 100 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 = avol1, avol1 = subarray(avol0, m6, # lpt), m = m7, m0 = n4 + # avol0[m6 + m8].data, m1 = m8, n0 = n, n1 = n2, ns = orphans, plog = log, avol0[m6 + m8].mapped?, m1 < # avol, m8 < # lpt, n3 < n, m6 + m8 < # avol0, 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(n4 + # buf0, 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 + n3 ≤ # buf, n2 + n ≤ # buf, n4 + # buf0 + n ≤ LEB_SIZE, ⌊err0⌋ , logoff ≠ LEB_SIZE → # buf3 = logoff ⊦ n3 = 0, m1 < # avol ∧ (avol[m1].mapped? → avol[m1].mapped? ∧ m1 < # avol)

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

Additional information

Used simplifier rules: ⊦ n0 < n → subarray(avol, m, n)[n0] = avol[m + n0]; (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