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Proof step 88 from proof write-inv-rec (previous step)

n0 + n = m0 * VFS_PAGE_SIZE + n2, files1 -- ino = files0 -- ino, VFS_PAGE_SIZE = n4 + n2 + m, files0[ino] = mkfile(m2, md0, m4, content), files1[ino] = mkfile(m2, md0, # links(ino, dirs), content0), afs-cons(dirs, files1), ino ∈ files0, ino ∈ files1, m0 * VFS_PAGE_SIZE ≤ # buf + n0, n0 + n ≤ n1, n1 ≤ # buf + n0, n ≤ # buf, n + m ≤ # buf, m0 * VFS_PAGE_SIZE ≤ n1 ⊦ #(((content.stream to n0) + (⌜buf⌝ to n) to n0 + n) from m0 * VFS_PAGE_SIZE) = ∞, #((⌜buf⌝ from n) to m) = ∞, n4 + m = 0, content.stream from (n0 + n) + n4 + m = content.stream from (n0 + n) + m from n4

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: stream, inst: buffer-inf name: from-from seq: ⊦ ¬ # σ0 < ⌜m + n⌝ → σ0 from m from n = σ0 from m + n subst: [n, m, σ0] → [n4, (n0 + n) + m, content.stream] flags: <all paths>

Additional information

Used simplifier rules: a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ # content.stream = ∞; (s)% ⊦ ⌜m + n⌝ = ⌜m⌝ + ⌜n⌝ ; (s)% ⊦ ¬ ∞ < n∞; (s) Used terms: n4, (n0 + n) + m, content.stream