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Proof step 52 from proof truncate-empty (previous step)

# content0[m0] = VFS_PAGE_SIZE, VFS_PAGE_SIZE = n0 + n1, files1[ino0] = mkfile(m, md0, # links(ino0, dirs), content0), n1 < VFS_PAGE_SIZE, afs-cons(dirs, files1), ino0 ∈ files1, m0 ∈ content0 ⊦ [asynced := ?] ( ( (content0.stream to m0 * VFS_PAGE_SIZE) + (((content0.stream from m0 * VFS_PAGE_SIZE) to VFS_PAGE_SIZE to n1) + (σ⊥ to n0)) + (content0.stream from VFS_PAGE_SIZE * m0 + VFS_PAGE_SIZE) to VFS_PAGE_SIZE * m0 + VFS_PAGE_SIZE) + σ⊥ from m0 * VFS_PAGE_SIZE + n1 = σ⊥), n0 = 0, n1 = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 53:
VFS_PAGE_SIZE = n0 + n1, files1[ino0] = mkfile(m, md0, # links(ino0, dirs), content0), n0 ≠ 0, n1 ≠ 0, n1 < VFS_PAGE_SIZE, afs-cons(dirs, files1), m0 ∈ content0, ino0 ∈ files1 ⊦ [asynced := ?] ( ( (content0.stream to m0 * VFS_PAGE_SIZE) + ((content0.stream from m0 * VFS_PAGE_SIZE) to n1) + (σ⊥ to n0) + (content0.stream from VFS_PAGE_SIZE * m0 + VFS_PAGE_SIZE) to VFS_PAGE_SIZE * m0 + VFS_PAGE_SIZE) + σ⊥ from m0 * VFS_PAGE_SIZE + n1 = σ⊥)

Rule argument

Additional information

Used simplifier rules: append-assoc: ⊦ (σ0 + σ3) + σ4 = σ0 + σ3 + σ4; from specification stream[buffer-inf]%¬ # σ0 < ⌜n⌝ ⊦ m < n → σ0 to n to m = σ0 to m; (s)% ⊦ ¬ ∞ < n∞; (s)% ⊦ #(content.stream from n) = ∞; (s)%⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, n0, content) ∧ n ∈ content → # content[n] = VFS_PAGE_SIZE; (s)