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Proof step 6 from proof refine-write (previous step)

# lpt = n1, # avol0 = n1 + m6, m6 + # lpt0 = # avol0, avol0[m2] = mapped(buf3), avol0[m3] = mapped(buf2), avol0[0] = mapped(buf1), subarray(avol0, m6, # lpt)[m] = mapped(buf0), avol = subarray(avol0, m6, # lpt), m < # lpt0, disk-layout(mksb(adr, m1, m2, m3, m4, m5, m6), # lpt0), ebm-vol-inv(avol0), ebm-vol-inv(subarray(avol0, m6, # lpt)), is-aligned(n, EB_PAGE_SIZE), is-aligned(m0, EB_PAGE_SIZE), is-encoded(lpt0, lebs(avol0, m5, lptlebs(# lpt0, LEB_SIZE))), is-encoded(mksb(adr, m1, 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(# lpt0, LEB_SIZE)), n0 + n ≤ # buf, m0 + n ≤ LEB_SIZE, # buf0 ≤ m0, m6 ≤ # avol0, logoff ≠ LEB_SIZE → # buf3 = logoff ⊦ ⟪persistence_io_write#(m, m0, n0, n, buf, mksb(adr, m1, m2, m3, m4, m5, m6); avol0; err)⟫ ⟨apersistence_io_write#(m, m0, n0, n, buf, adr, m1, log, lpt, orphans; avol; err0)⟩ ( # avol0 = m6 + (# avol0 - m6) ∧ avol = subarray(avol0, m6, # avol0 - m6) ∧ is-encoded(log, avol0[m2].data) ∧ is-encoded(lpt, lebs(avol0, m5, lptlebs(# avol0 - m6, LEB_SIZE))) ∧ is-encoded-pad(orphans, m4, avol0[m3].data) ∧ err = err0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
# avol0 = # lpt + m6, avol0[0] = mapped(buf1), avol0[m3] = mapped(buf2), avol0[m2] = mapped(buf3), avol0[m6 + m] = mapped(buf0), avol = subarray(avol0, m6, # lpt), m < # lpt, disk-layout(mksb(adr, m1, m2, m3, m4, m5, m6), # lpt), ebm-vol-inv(subarray(avol0, m6, # lpt)), ebm-vol-inv(avol0), is-aligned(m0, EB_PAGE_SIZE), is-aligned(n, EB_PAGE_SIZE), is-encoded(mksb(adr, m1, 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)), m6 ≤ # avol0, # buf0 ≤ m0, m0 + n ≤ LEB_SIZE, n0 + n ≤ # buf, logoff ≠ LEB_SIZE → # buf3 = logoff ⊦ ⟪persistence_io_write#(m, m0, n0, n, buf, mksb(adr, m1, m2, m3, m4, m5, m6); avol0; err)⟫ ⟨apersistence_io_write#(m, m0, n0, n, buf, adr, m1, log, lpt, orphans; avol; err0)⟩ ( # avol0 = m6 + (# avol0 - m6) ∧ avol = subarray(avol0, m6, # avol0 - m6) ∧ is-encoded(log, avol0[m2].data) ∧ is-encoded(lpt, lebs(avol0, m5, lptlebs(# avol0 - m6, LEB_SIZE))) ∧ is-encoded-pad(orphans, m4, avol0[m3].data) ∧ err = err0)

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%⊦ is-encoded(lpt0, buf) ∧ # lpt0 = # lpt1 → (is-encoded(lpt1, buf) ↔ lpt0 = lpt1); (s)% ⊦ n0 < n → subarray(avol, m, n)[n0] = avol[m + n0]; (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%eqs: ⊦ m = n + n0 ∧ m = n + n1 → n0 = n1; (forward) from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic