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Proof step 75 from proof inv-truncate (previous step)

VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, dirs[m] = mkdir(m6, md2, m7, m8, entries), files[m] = mkfile(m0, md, # links(m, dirs), content0), n1 * VFS_PAGE_SIZE < m2, n1 * VFS_PAGE_SIZE < n, afs-cons(dirs, files), m ∈ files, m2 / VFS_PAGE_SIZE ∈ content0, ROOT_INO ∈ dirs, n1 ∈ content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)], m2 ≤ n ⊦ # content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)][n1] = VFS_PAGE_SIZE, m2 % VFS_PAGE_SIZE = 0, buf-opt.some?, m ∈ dirs

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: store, inst: file-content name: At-other seq: ⊦ n ≠ n0 → content[n0, buf][n] = content[n] subst: [n, buf, n0, content] → [n1, fill (content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0), m2 / VFS_PAGE_SIZE, content0] flags: <all paths>

Additional information

Used simplifier rules: ⊦ n ≠ n0 → (n ∈ content[n0, buf] ↔ n ∈ content); (s)%⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, n0, content) ∧ n ∈ content → # content[n] = VFS_PAGE_SIZE; (s)% ⊦ content[n, buf][n] = buf; (s)% ⊦ # fill(buf, d, m, n) = # buf; (s) Used terms: n1, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0), m2 / VFS_PAGE_SIZE, content0