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Proof step 62 from proof truncate-same-iso (previous step)

VFS_PAGE_SIZE = n0 + n1, files0[ino0] = mkfile(m0 * VFS_PAGE_SIZE + n1, md, # links(ino0, dirs), content), n1 < VFS_PAGE_SIZE, afs-cons(dirs, files0), ino0 ∈ files0, m0 ∈ content ⊦ n0 = 0, n1 = 0, content.stream to m0 * VFS_PAGE_SIZE + n1 = (content.stream to m0 * VFS_PAGE_SIZE) + ((content.stream from m0 * VFS_PAGE_SIZE) to n1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 63:
⊦ ¬ # σ0 < ⌜n + n1⌝ → (σ0 to n) + ((σ0 from n) to n1) = σ0 to n + n1

Rule argument

spec: stream, inst: buffer-inf name: from-append-tofrom seq: ⊦ ¬ # σ0 < ⌜n + n1⌝ → (σ0 to n) + ((σ0 from n) to n1) = σ0 to n + n1 subst: [n1, n, σ0] → [n1, m0 * VFS_PAGE_SIZE, content.stream] flags: <all paths>

Additional information

Used simplifier rules: ⊦ # content.stream = ∞; (s)% ⊦ ⌜m + n⌝ = ⌜m⌝ + ⌜n⌝ ; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ ¬ ∞ < n∞; (s) Used terms: n1, m0 * VFS_PAGE_SIZE, content.stream