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Proof step 32 from proof recovery (previous step)

# 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))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 33:
⊦ avol0 ⊆ avol1 ↔ # avol0 = # avol1 ∧ (∀ m. m < # avol0 → (avol0[m].mapped? → avol1[m] = avol0[m]) ∧ (avol0[m] = unmapped ∧ avol1[m].mapped? → # avol1[m].data ≤ LEB_SIZE ∧ is-aligned(# avol1[m].data, EB_PAGE_SIZE)))
Proof step 34:
# avol0 = # avol, # avol0 = # lpt1 + m11, avol0[m2] = mapped(buf4), avol0[m3] = mapped(buf3), avol0[0] = mapped(buf2), m < # lpt1, 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(lpt1, lebs(avol0, m10, lptlebs(# lpt1, LEB_SIZE))), is-encoded(log1, buf4), is-encoded-pad(orphans0, m9, buf3), mapped-full?(avol0, m10, lptlebs(# lpt1, LEB_SIZE)), m11 ≤ # avol0, m1 ≠ LEB_SIZE → # buf4 = m1, logoff ≠ LEB_SIZE → # buf4 = logoff, ∀ m. m < # avol0 → (avol0[m].mapped? → avol[m] = avol0[m]) ∧ (avol0[m] = unmapped ∧ avol[m].mapped? → # avol[m].data ≤ LEB_SIZE ∧ is-aligned(# avol[m].data, EB_PAGE_SIZE)) ⊦ (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

spec: ebm-vol-inv name: ebm-vol-le seq: ⊦ avol0 ⊆ avol1 ↔ # avol0 = # avol1 ∧ (∀ m. m < # avol0 → (avol0[m].mapped? → avol1[m] = avol0[m]) ∧ ( avol0[m] = unmapped ∧ avol1[m].mapped? → # avol1[m].data ≤ LEB_SIZE ∧ is-aligned(# avol1[m].data, EB_PAGE_SIZE))) subst: [avol1, avol0] → [avol, avol0] flags: <all paths>

Additional information

Used terms: avol, avol0