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Proof step 97 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), 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)), n4 + # buf0 + n ≤ LEB_SIZE, n0 + n3 ≤ # buf, n0 + n ≤ # buf, ⌊err1⌋ , logoff ≠ LEB_SIZE → # buf3 = logoff ⊦ ⟨avol := subarray(avol0, m6, # lpt) [m8, mapped ( subarray(avol0, m6, # lpt)[m8].data + mkempbuf(n4 + # avol0[m6 + m8].data - # subarray(avol0, m6, # lpt)[m8].data) + subarray(buf, n0, n3)) ]⟩ ( 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)), m2 = m6 + m8, n3 = 0

Heuristic symbolic execution applied rule assign right

And closed the goal!

Rule argument

pos: right 1

Additional information

Used simplifier rules: ⊦ # subarray(avol, m, n) = n; (s)% ⊦ n0 < n → subarray(avol, m, n)[n0] = avol[m + n0]; (s)% ⊦ n ≥ m ↔ m ≤ n; (s)% ⊦ m ≤ m + n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m = m0 + n0 ∧ n < n0 → m0 + n < m; (s)% ⊦ mapped(buf).mapped?; (s)% ⊦ m ≤ m; (s)% ⊦ aleb.mapped? ↔ (∃ buf. aleb = mapped(buf)); (as)% ⊦ m + n - m = n; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ m ≠ n → avol[n, aleb][m] = avol[m]; (s)% ⊦ mapped(buf) = mapped(buf0) ↔ buf = buf0; (s)% ⊦ mapped(buf).data = buf; (s)% ⊦ is-encoded(nx0, buf) → (is-encoded(nx1, buf) ↔ nx0 = nx1); (s)%⊦ is-encoded-pad(ns0, n, buf) → (is-encoded-pad(ns1, n, buf) ↔ ns0 = ns1); (s)