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Proof step 127 from proof refine-write (previous step)

# avol0 = # lpt + m6, avol0[m6 + m8] = mapped(buf0), avol0[0] = mapped(buf1), avol0[m3] = mapped(buf2), avol0[m2] = mapped(buf3), avol1 = subarray(avol0, m6, # lpt), m8 < # 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(m7, 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)), m7 + n ≤ LEB_SIZE, m6 ≤ # avol0, # buf0 ≤ m7, n2 + n ≤ # buf, ⌊err0⌋ , logoff ≠ LEB_SIZE → # buf3 = logoff, ∀ n0. ¬ n0 < n ∨ ¬ is-aligned(n0, EB_PAGE_SIZE) ⊦ ⟨apersistence_io_write#(m8, m7, n2, n, buf, adr, m1, log, lpt, orphans; avol1; err1)⟩ ( avol1 = 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) ∧ err0 = err1)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 128:
# avol0 = # lpt + m6, # avol0 = n1 + m6, avol0[m2] = mapped(buf3), avol0[m3] = mapped(buf2), avol0[0] = mapped(buf1), avol0[m6 + m8] = mapped(buf0), avol1 = subarray(avol0, m6, # lpt), m8 < # lpt, disk-layout(mksb(adr, m1, 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(m7, EB_PAGE_SIZE), is-encoded(log, buf3), is-encoded(lpt, lebs(avol0, m5, lptlebs(# lpt, LEB_SIZE))), is-encoded(mksb(adr, m1, m2, m3, m4, m5, m6), buf1), is-encoded-pad(orphans, m4, buf2), mapped-full?(avol0, m5, lptlebs(# lpt, LEB_SIZE)), n2 + n ≤ # buf, # buf0 ≤ m7, m6 ≤ # avol0, m7 + n ≤ LEB_SIZE, ⌊err0⌋ , logoff ≠ LEB_SIZE → # buf3 = logoff, ∀ n0. ¬ n0 < n ∨ ¬ is-aligned(n0, EB_PAGE_SIZE) ⊦ ⟨apersistence_io_write#(m8, m7, n2, n, buf, adr, m1, log, lpt, orphans; avol1; err1)⟩ ( avol1 = subarray(avol0, m6, n1) ∧ is-encoded(log, avol0[m2].data) ∧ is-encoded(lpt, lebs(avol0, m5, lptlebs(n1, LEB_SIZE))) ∧ is-encoded-pad(orphans, m4, avol0[m3].data) ∧ err0 = err1)

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [# avol0, m6, n1]

Additional information

Used simplifier rules: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: # avol0, m6, n1