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Proof step 40 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), 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 + # buf0, EB_PAGE_SIZE), is-aligned(n, 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)), n2 + n ≤ # buf, n3 + # buf0 + n ≤ LEB_SIZE, logoff ≠ LEB_SIZE → # buf3 = logoff ⊦ n = 0, is-encoded(log, avol0[m6 + m8, mapped(buf0 + mkempbuf(n3) + subarray(buf, n2, n))][m2].data)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: array, inst: avolume name: Put-other seq: ⊦ m ≠ n → avol[n, aleb][m] = avol[m] subst: [m, aleb, n, avol] → [m2, mapped(buf0 + mkempbuf(n3) + subarray(buf, n2, n)), m6 + m8, avol0] flags: <all paths>

Additional information

Used simplifier rules: ⊦ EB_PAGE_SIZE ≠ 0; (s)% ⊦ mapped(buf).data = buf; (s)% ⊦ is-encoded(nx0, buf) → (is-encoded(nx1, buf) ↔ nx0 = nx1); (s)%m ≠ 0, is-aligned(n1, m) ⊦ is-aligned(n0 + n1, m) ↔ is-aligned(n0, m); (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ ¬ m + n < m; (s)%n ≤ n1 ⊦ ¬ disk-layout(mksb(adr, n0, n1, n2, m, n3, n), mainareasize); (s) Used terms: m2, mapped(buf0 + mkempbuf(n3) + subarray(buf, n2, n)), m6 + m8, avol0