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Proof step 47 from proof write-inv-post (previous step)

files1 -- ino = files0 -- ino, files0[ino] = mkfile(m1, md1, n2, content0), files1[ino] = mkfile(m1, md1, # links(ino, dirs), content1), (content0.stream from m1)[n3 - m1] = zero, m1 < n0, m1 < n0 + n, n3 < n0, n3 < n1, m1 < n1, n3 < # buf + n0, m1 < # buf + n0, n3 < n0 + n, afs-cons(dirs, files1), ino ∈ files1, ino ∈ files0, n ≤ # buf, n1 ≤ # buf + n0, n0 + n ≤ n1, m1 ≤ n3 ⊦ n = 0, zero = getbyte(n3, content0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 48:
files1 -- ino = files0 -- ino, (content0.stream from m1)[n4] = zero, files1[ino] = mkfile(m1, md1, # links(ino, dirs), content1), files0[ino] = mkfile(m1, md1, n2, content0), n3 = n4 + m1, n3 < n0 + n, m1 < # buf + n0, n3 < # buf + n0, m1 < n1, n3 < n1, n3 < n0, m1 < n0 + n, m1 < n0, afs-cons(dirs, files1), ino ∈ files0, ino ∈ files1, m1 ≤ n3, n0 + n ≤ n1, n1 ≤ # buf + n0, n ≤ # buf ⊦ n = 0, zero = getbyte(n3, content0)

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [n, m, n0] → [m1, n3, n4]

Additional information

Used simplifier rules: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: m1, n3, n4