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Proof step 5 from proof write-inv-rec (previous step)

files0[ino] = mkfile(m2, md0, m4, content), files1[ino] = mkfile(m5, md1, m6, content0), write-inv(n0, n1, mkinode(ino, md, boolvar, m0, m3, m1), buf, n, dirs, files0, files1), n + m ≤ # buf, m + (n0 + n) % VFS_PAGE_SIZE ≤ VFS_PAGE_SIZE ⊦ write-inv (n0, n1, buf, n + m, content, content0[(n0 + n) / VFS_PAGE_SIZE, copy(buf, n, getpage((n0 + n) / VFS_PAGE_SIZE, content0), (n0 + n) % VFS_PAGE_SIZE, m)])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ write-inv(n0, n1, buf, n, content0, content1) ↔ content1.stream = (content0.stream to n0) + (⌜buf⌝ to n) + (content0.stream from n0 + n)
Proof step 7:
files1[ino] = mkfile(m5, md1, m6, content0), files0[ino] = mkfile(m2, md0, m4, content), write-inv(n0, n1, mkinode(ino, md, boolvar, m0, m3, m1), buf, n, dirs, files0, files1), m + (n0 + n) % VFS_PAGE_SIZE ≤ VFS_PAGE_SIZE, n + m ≤ # buf ⊦ content0[(n0 + n) / VFS_PAGE_SIZE, copy(buf, n, getpage((n0 + n) / VFS_PAGE_SIZE, content0), (n0 + n) % VFS_PAGE_SIZE, m)].stream = (content.stream to n0) + (⌜buf⌝ to n + m) + (content.stream from n0 + n + m)

Rule argument

spec: <toplevel> name: write-inv seq: ⊦ write-inv(n0, n1, buf, n, content0, content1) ↔ content1.stream = (content0.stream to n0) + (⌜buf⌝ to n) + (content0.stream from n0 + n) subst: [content1, content0, n, buf, n1, n0] → [content0 [(n0 + n) / VFS_PAGE_SIZE, copy (buf, n, getpage((n0 + n) / VFS_PAGE_SIZE, content0), (n0 + n) % VFS_PAGE_SIZE, m) ], content, n + m, buf, n1, n0] flags: <all paths>

Additional information

Used terms: content0 [(n0 + n) / VFS_PAGE_SIZE, copy (buf, n, getpage((n0 + n) / VFS_PAGE_SIZE, content0), (n0 + n) % VFS_PAGE_SIZE, m) ], content, n + m, buf, n1, n0