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Proof step 62 from proof inv-write (previous step)

# avols[v][m2].data = LEB_SIZE, LEB_SIZE = (n3 + n1) + m1, LEB_SIZE = n0 + avols[v][m2].fill, avols[v][m2].mapped?, m2 < # avols[v], n1 < n, ebm-cons(avols), is-aligned(n, EB_PAGE_SIZE), is-aligned(m1, EB_PAGE_SIZE), is-aligned(n1, 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, m1 ≤ LEB_SIZE, n + n2 ≤ # buf, m1 + n ≤ LEB_SIZE, n2 + n1 ≤ # buf, avols[v][m2].fill ≤ LEB_SIZE, avols[v][m2].fill ≤ m1, n1 + m1 ≤ LEB_SIZE, ⌊err0⌋ ⊦ n1 = 0, range=(subarray(avols[v][m2].data, 0, m1) + subarray(buf, n2, n1) + mkempbuf(n3), m1 + n1, emptyleb, 0, LEB_SIZE - m1 + n1)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 63:
# avols[v][m2].data = LEB_SIZE, LEB_SIZE = n0 + avols[v][m2].fill, LEB_SIZE = (n3 + n1) + m1, LEB_SIZE = n4 + m1 + n1, avols[v][m2].mapped?, n1 < n, m2 < # avols[v], ebm-cons(avols), is-aligned(avols[v][m2].fill, EB_PAGE_SIZE), is-aligned(n1, 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, n1 + m1 ≤ LEB_SIZE, avols[v][m2].fill ≤ m1, avols[v][m2].fill ≤ LEB_SIZE, n2 + n1 ≤ # buf, m1 + n ≤ LEB_SIZE, n + n2 ≤ # buf, m1 ≤ LEB_SIZE, m1 + n1 ≤ LEB_SIZE, ⌊err0⌋ ⊦ n1 = 0, range=(subarray(avols[v][m2].data, 0, m1) + subarray(buf, n2, n1) + mkempbuf(n3), m1 + n1, emptyleb, 0, n4)

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [LEB_SIZE, m1 + n1, n4]

Additional information

Used simplifier rules: c: ⊦ m + n = n + m; from specification nat-basic%n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: LEB_SIZE, m1 + n1, n4