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Proof step 31 from proof recovery (previous step)

# avol0 = # lpt1 + m11, avol0[0] = mapped(buf2), avol0[m3] = mapped(buf3), avol0[m2] = mapped(buf4), disk-layout(mksb(adr0, m0, m2, m3, m9, m10, m11), # lpt1), ebm-vol-inv(avol0), ebm-vol-inv(subarray(avol0, m11, # lpt1)), is-encoded(log1, buf4), is-encoded(lpt1, lebs(avol0, m10, lptlebs(# lpt1, 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 ⊦ # subarray(avol0, m11, # lpt1) = # subarray(avol, m11, # lpt1) ∧ (∀ m. m < # subarray(avol0, m11, # lpt1) → (subarray(avol0, m11, # lpt1)[m].mapped? → subarray(avol, m11, # lpt1)[m] = subarray(avol0, m11, # lpt1)[m]) ∧ ( subarray(avol0, m11, # lpt1)[m] = unmapped ∧ subarray(avol, m11, # lpt1)[m].mapped? → # subarray(avol, m11, # lpt1)[m].data ≤ LEB_SIZE ∧ is-aligned(# subarray(avol, m11, # lpt1)[m].data, EB_PAGE_SIZE)))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 32:
# avol0 = # lpt1 + m11, avol0[0] = mapped(buf2), avol0[m3] = mapped(buf3), avol0[m2] = mapped(buf4), m < # lpt1, disk-layout(mksb(adr0, m0, m2, m3, m9, m10, m11), # lpt1), ebm-vol-inv(avol0), ebm-vol-inv(subarray(avol0, m11, # lpt1)), is-encoded(log1, buf4), is-encoded(lpt1, lebs(avol0, m10, lptlebs(# lpt1, 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 ⊦ (avol0[m11 + m].mapped? → avol[m11 + m] = avol0[m11 + m]) ∧ (avol0[m11 + m] = unmapped ∧ avol[m11 + m].mapped? → # avol[m11 + m].data ≤ LEB_SIZE ∧ is-aligned(# avol[m11 + m].data, EB_PAGE_SIZE))

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ n0 < n → subarray(avol, m, n)[n0] = avol[m + n0]; (s)% ⊦ # subarray(avol, m, n) = n; (s)