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Proof step 86 from proof truncate-inv (previous step)

# fill(content0[m2], zero, n0, n1) = VFS_PAGE_SIZE, VFS_PAGE_SIZE = n1 + 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, n1)] 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, n1)] upto (m2 * VFS_PAGE_SIZE + n0)) ], ino4 ∈ files2, m2 ∈ content0 ⊦ ( (content0.stream to m2 * VFS_PAGE_SIZE) + ⌜fill(content0[m2], zero, n0, n1)⌝ + (content0.stream from (m2 + 1) * VFS_PAGE_SIZE) to VFS_PAGE_SIZE * m2 + VFS_PAGE_SIZE) + σ⊥ from m2 * VFS_PAGE_SIZE + n0 = σ⊥, n0 = 0, n1 = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 87:
VFS_PAGE_SIZE = n1 + 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, n1)] 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, n1)] upto (m2 * VFS_PAGE_SIZE + n0)) ], m2 ∈ content0, ino4 ∈ files2 ⊦ ( (content0.stream to m2 * VFS_PAGE_SIZE) + ⌜fill(content0[m2], zero, n0, n1)⌝ + (content0.stream from VFS_PAGE_SIZE * m2 + VFS_PAGE_SIZE) to VFS_PAGE_SIZE * m2 + VFS_PAGE_SIZE) + σ⊥ from m2 * VFS_PAGE_SIZE + n0 = σ⊥, n0 = 0, n1 = 0

Rule argument

Additional information

Used simplifier rules: append-assoc: ⊦ (σ0 + σ3) + σ4 = σ0 + σ3 + σ4; from specification stream[buffer-inf]%mult-c: ⊦ m * n = n * m; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m * (n + 1) = m * n + m; (s)%⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, n0, content) ∧ n ∈ content → # content[n] = VFS_PAGE_SIZE; (s)% ⊦ # fill(buf, d, m, n) = # buf; (s)