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Proof step 7 from proof mapped-full-aligndown-vol (previous step)

# 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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
# avol0 = # avol1, # buf = LEB_SIZE, avol0[n0] = mapped(buf), n0 < n + m, n0 < # avol1, n < # avol1, n ≤ n0, ∀ m. m < # avol1 → (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

Additional information

Used simplifier rules: lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic