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Proof step 42 from proof writepage-afs-cons (previous step)

# buf2 = VFS_PAGE_SIZE, files[m] = mkfile(m0, md, # links(m, dirs), content), dirs[m] = mkdir(m5, md2, m6, m7, entries), afs-cons(dirs, files), m ∈ files, ROOT_INO ∈ dirs, n0 ∈ content[pageno, copy(buf0, ino0, buf2, ino, n)], ino0 + n ≤ # buf0, ino + n ≤ VFS_PAGE_SIZE ⊦ # content[pageno, copy(buf0, ino0, buf2, ino, n)][n0] = VFS_PAGE_SIZE, 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] → [n0, copy(buf0, ino0, buf2, ino, n), pageno, content] 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)% ⊦ # copy(buf, m, buf0, m0, n) = # buf0; (s) Used terms: n0, copy(buf0, ino0, buf2, ino, n), pageno, content