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Proof step 98 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 ⊦ ( ( (content0.stream to m2 * VFS_PAGE_SIZE) + ((content0.stream from m2 * VFS_PAGE_SIZE) to n0) + (σ⊥ to n2) + (content0.stream from VFS_PAGE_SIZE * m2 + VFS_PAGE_SIZE) from m2 * VFS_PAGE_SIZE + n0) to n2) + σ⊥ = σ⊥, n0 = 0, n2 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 99:
⊦ ¬ ⌜m⌝ < # σ1 → σ1 + σ2 from m = σ2 from (m - (# σ1).n)
Proof step 100:
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 ⊦ ( ( ((content0.stream from m2 * VFS_PAGE_SIZE) to n0) + (σ⊥ to n2) + (content0.stream from VFS_PAGE_SIZE * m2 + VFS_PAGE_SIZE) from (m2 * VFS_PAGE_SIZE + n0 - (#(content0.stream to m2 * VFS_PAGE_SIZE)).n)) to n2) + σ⊥ = σ⊥, n0 = 0, n2 = 0, ⌜m2 * VFS_PAGE_SIZE + n0⌝ < #(content0.stream to m2 * VFS_PAGE_SIZE)

Rule argument

spec: stream, inst: buffer-inf name: append-from-ge-02 seq: ⊦ ¬ ⌜m⌝ < # σ1 → σ1 + σ2 from m = σ2 from (m - (# σ1).n) subst: [m, σ2, σ1] → [m2 * VFS_PAGE_SIZE + n0, ((content0.stream from m2 * VFS_PAGE_SIZE) to n0) + (σ⊥ to n2) + (content0.stream from VFS_PAGE_SIZE * m2 + VFS_PAGE_SIZE), content0.stream to m2 * VFS_PAGE_SIZE] flags: <all paths>

Additional information

Used simplifier rules: ⊦ ⌜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% ⊦ # content.stream = ∞; (s)% ⊦ ¬ ∞ < n∞; (s)%¬ # σ0 < ⌜n⌝ ⊦ #(σ0 to n) = ⌜n⌝ ; (s)% ⊦ ⌜n⌝ + ⌜m⌝ < ⌜n0⌝ ↔ n + m < n0; (s)% ⊦ n0 < m0 → (m0 * m + n0 < m0 * n ↔ m < n); (s)% ⊦ ¬ n < n; (s)%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult%add-assoc: ⊦ (n∞ + n∞1) + n∞2 = n∞ + n∞1 + n∞2; from specification nat-inf%add-comm: ⊦ n∞1 + n∞2 = n∞2 + n∞1; from specification nat-inf Used terms: m2 * VFS_PAGE_SIZE + n0, ((content0.stream from m2 * VFS_PAGE_SIZE) to n0) + (σ⊥ to n2) + (content0.stream from VFS_PAGE_SIZE * m2 + VFS_PAGE_SIZE), content0.stream to m2 * VFS_PAGE_SIZE