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Proof step 59 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) + (σ⊥ to n0) + (content.stream from VFS_PAGE_SIZE * m0 + VFS_PAGE_SIZE) to n1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 60:
⊦ ¬ # σ1 < ⌜n⌝ → σ1 + σ2 to n = σ1 to n
Proof step 61:
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), m0 ∈ content, ino0 ∈ files0 ⊦ 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 to n1), #((content.stream from m0 * VFS_PAGE_SIZE) to n1) < ⌜n1⌝

Rule argument

spec: stream, inst: buffer-inf name: append-to-ls seq: ⊦ ¬ # σ1 < ⌜n⌝ → σ1 + σ2 to n = σ1 to n subst: [n, σ2, σ1] → [n1, (σ⊥ to n0) + (content.stream from VFS_PAGE_SIZE * m0 + VFS_PAGE_SIZE), (content.stream from m0 * VFS_PAGE_SIZE) to n1] flags: <all paths>

Additional information

Used simplifier rules: ⊦ #(content.stream from n) = ∞; (s)% ⊦ ¬ ∞ < n∞; (s)%¬ # σ0 < ⌜n⌝ ⊦ #(σ0 to n) = ⌜n⌝ ; (s)% ⊦ ⌜m⌝ < ⌜n⌝ ↔ m < n; (s)% ⊦ ¬ n < n; (s) Used terms: n1, (σ⊥ to n0) + (content.stream from VFS_PAGE_SIZE * m0 + VFS_PAGE_SIZE), (content.stream from m0 * VFS_PAGE_SIZE) to n1