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Proof step 23 from proof recovery (previous step)

# lpt = # avol0 - m11, # avol0 = # lpt1 + m11, avol0[0] = mapped(buf2), avol0[m3] = mapped(buf3), avol0[m2] = mapped(buf4), lebs(avol, m10, lptlebs(# lpt, LEB_SIZE)) = lebs(avol0, m10, lptlebs(# lpt, LEB_SIZE)), log0 = log1, ns0 = orphans0, disk-layout(mksb(adr0, m0, m2, m3, m9, m10, m11), # lpt1), ebm-vol-inv(avol0), ebm-vol-inv(subarray(avol0, m11, # lpt1)), is-encoded(lpt1, lebs(avol0, m10, lptlebs(# lpt1, LEB_SIZE))), is-encoded(log1, buf4), is-encoded(lpt, lebs(avol0, m10, lptlebs(# lpt, LEB_SIZE))), is-encoded(mksb(adr0, m0, m2, m3, m9, m10, m11), buf2), is-encoded-pad(orphans0, m9, buf3), mapped-full?(avol0, m10, lptlebs(# lpt1, LEB_SIZE)), m11 ≤ # avol0, avol0 ⊆ avol, logoff ≠ LEB_SIZE → # buf4 = logoff, m1 ≠ LEB_SIZE → # buf4 = m1 ⊦ ∃ avol1. subarray(avol0, m11, # lpt1) ⊆ avol1 ∧ ⟨adr := adr0, m := m0; apersistence_io_recover#(; adr2, m5, ns1, log2, lpt2, adr, m, log0, lpt1, ns0, avol1; err0)⟩ ( m = m5 ∧ adr = adr2 ∧ avol1 = subarray(avol, m11, # avol0 - m11) ∧ log2 = log0 ∧ is-encoded(lpt1, lebs(avol, m10, lptlebs(# avol0 - m11, LEB_SIZE))) ∧ ns1 = ns0 ∧ adr0 = adr2 ∧ m0 = m5 ∧ orphans0 = ns0 ∧ log1 = log0 ∧ lpt = lpt2 ∧ ESUCCESS = err0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 24:
# avol0 = # lpt1 + m11, # lpt = n0, # avol0 = n0 + m11, avol0[m2] = mapped(buf4), avol0[m3] = mapped(buf3), avol0[0] = mapped(buf2), lebs(avol, m10, lptlebs(# lpt, LEB_SIZE)) = lebs(avol0, m10, lptlebs(# lpt, LEB_SIZE)), log0 = log1, ns0 = orphans0, disk-layout(mksb(adr0, m0, m2, m3, m9, m10, m11), # lpt1), ebm-vol-inv(subarray(avol0, m11, # lpt1)), ebm-vol-inv(avol0), is-encoded(mksb(adr0, m0, m2, m3, m9, m10, m11), buf2), is-encoded(lpt, lebs(avol0, m10, lptlebs(# lpt, LEB_SIZE))), is-encoded(log1, buf4), is-encoded(lpt1, lebs(avol0, m10, lptlebs(# lpt1, LEB_SIZE))), is-encoded-pad(orphans0, m9, buf3), mapped-full?(avol0, m10, lptlebs(# lpt1, LEB_SIZE)), m11 ≤ # avol0, avol0 ⊆ avol, m1 ≠ LEB_SIZE → # buf4 = m1, logoff ≠ LEB_SIZE → # buf4 = logoff ⊦ ∃ avol1. subarray(avol0, m11, # lpt1) ⊆ avol1 ∧ ⟨adr := adr0, m := m0; apersistence_io_recover#(; adr2, m5, ns1, log2, lpt2, adr, m, log0, lpt1, ns0, avol1; err0)⟩ ( m = m5 ∧ adr = adr2 ∧ avol1 = subarray(avol, m11, n0) ∧ log2 = log0 ∧ is-encoded(lpt1, lebs(avol, m10, lptlebs(n0, LEB_SIZE))) ∧ ns1 = ns0 ∧ adr0 = adr2 ∧ m0 = m5 ∧ orphans0 = ns0 ∧ log1 = log0 ∧ lpt = lpt2 ∧ ESUCCESS = err0)

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [n, m, n0] → [m11, # avol0, n]

Additional information

Used simplifier rules: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: m11, # avol0, n