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Proof step 104 from proof truncate-inv (previous step)

VFS_PAGE_SIZE = n2 + n0, files2[ino4] = mkfile(m2 * VFS_PAGE_SIZE + n0, md, # links(ino4, dirs0), content0), n0 < VFS_PAGE_SIZE, afs-cons(dirs0, files2), afs-cons (dirs0, files2 [ino4, mkfile(m2 * VFS_PAGE_SIZE + n0, md, # links(ino4, dirs0), content0[m2, fill(content0[m2], zero, n0, n2)] upto (m2 * VFS_PAGE_SIZE + n0)) ]), files2 ~ files2 [ino4, mkfile(m2 * VFS_PAGE_SIZE + n0, md, # links(ino4, dirs0), content0[m2, fill(content0[m2], zero, n0, n2)] upto (m2 * VFS_PAGE_SIZE + n0)) ], ino4 ∈ files2, m2 ∈ content0 ⊦ ((σ⊥ to n2) + (content0.stream from VFS_PAGE_SIZE * m2 + VFS_PAGE_SIZE) to n2) + σ⊥ = σ⊥, n0 = 0, n2 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 105:
⊦ ¬ # σ1 < ⌜n⌝ → σ1 + σ2 to n = σ1 to n
Proof step 106:
VFS_PAGE_SIZE = n2 + n0, files2[ino4] = mkfile(m2 * VFS_PAGE_SIZE + n0, md, # links(ino4, dirs0), content0), n0 < VFS_PAGE_SIZE, afs-cons (dirs0, files2 [ino4, mkfile(m2 * VFS_PAGE_SIZE + n0, md, # links(ino4, dirs0), content0[m2, fill(content0[m2], zero, n0, n2)] upto (m2 * VFS_PAGE_SIZE + n0)) ]), afs-cons(dirs0, files2), files2 ~ files2 [ino4, mkfile(m2 * VFS_PAGE_SIZE + n0, md, # links(ino4, dirs0), content0[m2, fill(content0[m2], zero, n0, n2)] upto (m2 * VFS_PAGE_SIZE + n0)) ], m2 ∈ content0, ino4 ∈ files2 ⊦ (σ⊥ to n2 to n2) + σ⊥ = σ⊥, n0 = 0, n2 = 0, #(σ⊥ to n2) < ⌜n2⌝

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] → [n2, content0.stream from VFS_PAGE_SIZE * m2 + VFS_PAGE_SIZE, σ⊥ to n2] flags: <all paths>

Additional information

Used simplifier rules: ⊦ # σ⊥ = ∞; (s)% ⊦ ¬ ∞ < n∞; (s)%¬ # σ0 < ⌜n⌝ ⊦ #(σ0 to n) = ⌜n⌝ ; (s)% ⊦ ⌜m⌝ < ⌜n⌝ ↔ m < n; (s)% ⊦ ¬ n < n; (s) Used terms: n2, content0.stream from VFS_PAGE_SIZE * m2 + VFS_PAGE_SIZE, σ⊥ to n2