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Proof step 5 from proof mapped-full-aligndown-vol (previous step)

# buf = LEB_SIZE, avol0[n0] = mapped(buf), n < # avol0, n0 < # avol0, n0 < # avol1, n0 < n + m, n < # avol1, n ≤ n0, avol0 ⊆ avol1 ⊦ m = 0, avol1[n0].mapped? ∧ # avol1[n0].data = LEB_SIZE

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ 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 7:
# avol0 = # avol1, # buf = LEB_SIZE, avol0[n0] = mapped(buf), n < # avol1, n0 < n + m, n0 < # avol1, n0 < # avol0, n < # avol0, n ≤ n0, ∀ 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)) ⊦ m = 0, avol1[n0].mapped? ∧ # avol1[n0].data = LEB_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] → [avol1, avol0] flags: <all paths>

Additional information

Used terms: avol1, avol0