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Proof step 20 from proof inv-write (previous step)

m6 + # lpt = # avol, avol[m6 + m8] = mapped(buf0), avol[0] = mapped(buf1), avol[m3] = mapped(buf2), avol[m2] = mapped(buf3), err0 = ESUCCESS, avol[m6 + m8].mapped?, m6 + m8 < # avol, m8 < # lpt, disk-layout(mksb(adr, m1, m2, m3, m4, m5, m6), # lpt), ebm-vol-inv(avol[m6 + m8, mapped(avol[m6 + m8].data + mkempbuf(m7 - # avol[m6 + m8].data) + subarray(buf, n2, n))]), ebm-vol-inv(avol), is-aligned(m7, EB_PAGE_SIZE), is-aligned(n, EB_PAGE_SIZE), is-encoded(log, buf3), is-encoded(lpt, lebs(avol, m5, lptlebs(# lpt, LEB_SIZE))), is-encoded(mksb(adr, m1, m2, m3, m4, m5, m6), buf1), is-encoded-pad(orphans, m4, buf2), mapped-full?(avol, m5, lptlebs(# lpt, LEB_SIZE)), m7 + n ≤ LEB_SIZE, n2 + n ≤ # buf, # buf0 ≤ m7, m7 ≥ # avol[m6 + m8].data, logoff ≠ LEB_SIZE → # buf3 = logoff, ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ n = 0, ∃ lpt0, log, orphans. disk-layout(mksb(adr, m1, m2, m3, m4, m5, m6), # lpt0) ∧ m6 + # lpt0 = # avol[m6 + m8, mapped(avol[m6 + m8].data + mkempbuf(m7 - # avol[m6 + m8].data) + subarray(buf, n2, n))] ∧ avol[m6 + m8, mapped(avol[m6 + m8].data + mkempbuf(m7 - # avol[m6 + m8].data) + subarray(buf, n2, n))][0].mapped? ∧ is-encoded (mksb(adr, m1, m2, m3, m4, m5, m6), avol[m6 + m8, mapped(avol[m6 + m8].data + mkempbuf(m7 - # avol[m6 + m8].data) + subarray(buf, n2, n))][0].data) ∧ avol[m6 + m8, mapped(avol[m6 + m8].data + mkempbuf(m7 - # avol[m6 + m8].data) + subarray(buf, n2, n))][m3].mapped? ∧ is-encoded-pad(orphans, m4, avol[m6 + m8, mapped(avol[m6 + m8].data + mkempbuf(m7 - # avol[m6 + m8].data) + subarray(buf, n2, n))][m3].data) ∧ avol[m6 + m8, mapped(avol[m6 + m8].data + mkempbuf(m7 - # avol[m6 + m8].data) + subarray(buf, n2, n))][m2].mapped? ∧ ( logoff ≠ LEB_SIZE → # avol[m6 + m8, mapped(avol[m6 + m8].data + mkempbuf(m7 - # avol[m6 + m8].data) + subarray(buf, n2, n))][m2].data = logoff) ∧ is-encoded(log, avol[m6 + m8, mapped(avol[m6 + m8].data + mkempbuf(m7 - # avol[m6 + m8].data) + subarray(buf, n2, n))][m2].data) ∧ mapped-full? (avol[m6 + m8, mapped(avol[m6 + m8].data + mkempbuf(m7 - # avol[m6 + m8].data) + subarray(buf, n2, n))], m5, lptlebs(# lpt0, LEB_SIZE)) ∧ is-encoded (lpt0, lebs (avol[m6 + m8, mapped(avol[m6 + m8].data + mkempbuf(m7 - # avol[m6 + m8].data) + subarray(buf, n2, n))], m5, lptlebs(# lpt0, LEB_SIZE)))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 21:
m6 + # lpt = # avol, avol[m6 + m8] = mapped(buf0), avol[m2] = mapped(buf3), avol[m3] = mapped(buf2), avol[0] = mapped(buf1), m8 < # lpt, disk-layout(mksb(adr, m1, m2, m3, m4, m5, m6), # lpt), ebm-vol-inv(avol), ebm-vol-inv(avol[m6 + m8, mapped(buf0 + mkempbuf(m7 - # buf0) + subarray(buf, n2, n))]), is-aligned(n, EB_PAGE_SIZE), is-aligned(m7, EB_PAGE_SIZE), is-encoded(mksb(adr, m1, m2, m3, m4, m5, m6), buf1), is-encoded(lpt, lebs(avol, m5, lptlebs(# lpt, LEB_SIZE))), is-encoded(log, buf3), is-encoded-pad(orphans, m4, buf2), mapped-full?(avol, m5, lptlebs(# lpt, LEB_SIZE)), # buf0 ≤ m7, n2 + n ≤ # buf, m7 + n ≤ LEB_SIZE, logoff ≠ LEB_SIZE → # buf3 = logoff ⊦ n = 0, ∃ lpt0, log0. m6 + # lpt0 = # avol ∧ avol[m6 + m8, mapped(buf0 + mkempbuf(m7 - # buf0) + subarray(buf, n2, n))][0].mapped? ∧ is-encoded(mksb(adr, m1, m2, m3, m4, m5, m6), avol[m6 + m8, mapped(buf0 + mkempbuf(m7 - # buf0) + subarray(buf, n2, n))][0].data) ∧ avol[m6 + m8, mapped(buf0 + mkempbuf(m7 - # buf0) + subarray(buf, n2, n))][m2].mapped? ∧ (logoff ≠ LEB_SIZE → # avol[m6 + m8, mapped(buf0 + mkempbuf(m7 - # buf0) + subarray(buf, n2, n))][m2].data = logoff) ∧ is-encoded(log0, avol[m6 + m8, mapped(buf0 + mkempbuf(m7 - # buf0) + subarray(buf, n2, n))][m2].data) ∧ mapped-full?(avol[m6 + m8, mapped(buf0 + mkempbuf(m7 - # buf0) + subarray(buf, n2, n))], m5, lptlebs(# lpt0, LEB_SIZE)) ∧ is-encoded(lpt0, lebs(avol[m6 + m8, mapped(buf0 + mkempbuf(m7 - # buf0) + subarray(buf, n2, n))], m5, lptlebs(# lpt0, LEB_SIZE)))

Rule argument

Additional information

Used simplifier rules: ⊦ is-encoded-pad(ns0, n, buf) → (is-encoded-pad(ns1, n, buf) ↔ ns0 = ns1); (s)% ⊦ mapped(buf).mapped?; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ mapped(buf).data = buf; (s)% ⊦ mapped(buf) = mapped(buf0) ↔ buf = buf0; (s)%m ≠ n ⊦ avol[m, aleb][n] = avol[n]; (s)%⊦ disk-layout(mksb(adr, m0, m1, m2, m, m3, m4), mainareasize) → m4 + n ≠ m2; (s)%m = n ⊦ disk-layout(sb, m) → disk-layout(sb, n); (s)%eqs: ⊦ m = n + n0 ∧ m = n + n1 → n0 = n1; (forward) from specification nat-basic% ⊦ # avol[n, aleb] = # avol; (s)% ⊦ ¬ ⌊ESUCCESS⌋ ; (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% ⊦ n ≥ m ↔ m ≤ n; (s)