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Proof step 20 from proof inv-write (previous step)

# avols[v][m2].data = LEB_SIZE, LEB_SIZE = (n1 + n) + m1, LEB_SIZE = n0 + avols[v][m2].fill, avols[v][m2].mapped?, m2 < # avols[v], ebm-cons(avols), is-aligned(avols[v][m2].fill, EB_PAGE_SIZE), is-aligned(m1, EB_PAGE_SIZE), is-aligned(n, EB_PAGE_SIZE), range=(avols[v][m2].data, avols[v][m2].fill, emptyleb, 0, n0), v ∈ avols, avols[v][m2].fill ≤ LEB_SIZE, m1 ≤ LEB_SIZE, n2 + n ≤ # buf, m1 + n ≤ LEB_SIZE, n + n2 ≤ # buf, avols[v][m2].fill ≤ m1, n + m1 ≤ LEB_SIZE ⊦ n = 0, range=(subarray(avols[v][m2].data, 0, m1) + subarray(buf, n2, n) + mkempbuf(n1), m1 + n, emptyleb, 0, LEB_SIZE - m1 + n)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 21:
# avols[v][m2].data = LEB_SIZE, LEB_SIZE = n0 + avols[v][m2].fill, LEB_SIZE = (n1 + n) + m1, LEB_SIZE = n3 + m1 + n, avols[v][m2].mapped?, m2 < # avols[v], ebm-cons(avols), is-aligned(n, EB_PAGE_SIZE), is-aligned(m1, EB_PAGE_SIZE), is-aligned(avols[v][m2].fill, EB_PAGE_SIZE), range=(avols[v][m2].data, avols[v][m2].fill, emptyleb, 0, n0), v ∈ avols, n + m1 ≤ LEB_SIZE, avols[v][m2].fill ≤ m1, n + n2 ≤ # buf, m1 + n ≤ LEB_SIZE, n2 + n ≤ # buf, m1 ≤ LEB_SIZE, avols[v][m2].fill ≤ LEB_SIZE ⊦ n = 0, range=(subarray(avols[v][m2].data, 0, m1) + subarray(buf, n2, n) + mkempbuf(n1), m1 + n, emptyleb, 0, n3)

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [LEB_SIZE, m1 + n, n3]

Additional information

Used simplifier rules: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: LEB_SIZE, m1 + n, n3