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Proof step 26 from proof write-inv-strong-rec (previous step)

files0[ino] = mkfile(m, md1, m5, content0), files1[ino] = mkfile(m2, md0, m3, content), write-inv(n0, n1, mkinode(ino, md, boolvar, m0, m4, m1), buf, n, dirs, files0, files1), ino ∈ files1, (n0 + n) % VFS_PAGE_SIZE + min(n1 - n0 + n, n2) ≤ VFS_PAGE_SIZE ⊦ write-inv (n0, n1, buf, n + min(n1 - n0 + n, n2), content0, content[(n0 + n) / VFS_PAGE_SIZE, copy(buf, n, getpage((n0 + n) / VFS_PAGE_SIZE, content), (n0 + n) % VFS_PAGE_SIZE, min(n1 - n0 + n, n2))])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 27:
write-inv(n0, n1, mkinode(ino, md, boolvar, m0, m3, m1), buf, n, dirs, files0, files1), files0[ino].content = content0, files1[ino].content = content1, n + m ≤ # buf, m + (n0 + n) % VFS_PAGE_SIZE ≤ VFS_PAGE_SIZE ⊦ write-inv (n0, n1, buf, n + m, content0, content1[(n0 + n) / VFS_PAGE_SIZE, copy(buf, n, getpage((n0 + n) / VFS_PAGE_SIZE, content1), (n0 + n) % VFS_PAGE_SIZE, m)])
Proof step 28:
files1[ino] = mkfile(m2, md0, m3, content), files0[ino] = mkfile(m, md1, m5, content0), write-inv(n0, n1, mkinode(ino, md, boolvar, m0, m4, m1), buf, n, dirs, files0, files1), ino ∈ files1, (n0 + n) % VFS_PAGE_SIZE + min(n1 - n0 + n, n2) ≤ VFS_PAGE_SIZE ⊦ write-inv (n0, n1, buf, n + min(n1 - n0 + n, n2), content0, content[(n0 + n) / VFS_PAGE_SIZE, copy(buf, n, getpage((n0 + n) / VFS_PAGE_SIZE, content), (n0 + n) % VFS_PAGE_SIZE, min(n1 - n0 + n, n2))]), write-inv(n0, n1, mkinode(ino, md, boolvar, m0, m4, m1), buf, n, dirs, files0, files1) ∧ files0[ino].content = content0 ∧ files1[ino].content = content ∧ n + min(n1 - n0 + n, n2) ≤ # buf ∧ min(n1 - n0 + n, n2) + (n0 + n) % VFS_PAGE_SIZE ≤ VFS_PAGE_SIZE

Rule argument

spec: <toplevel> name: write-inv-rec seq: write-inv (n0, n1, mkinode(ino, md, boolvar, m0, m3, m1), buf, n, dirs, files0, files1), files0[ino].content = content0, files1[ino].content = content1, n + m ≤ # buf, m + (n0 + n) % VFS_PAGE_SIZE ≤ VFS_PAGE_SIZE ⊦ write-inv (n0, n1, buf, n + m, content0, content1 [(n0 + n) / VFS_PAGE_SIZE, copy (buf, n, getpage((n0 + n) / VFS_PAGE_SIZE, content1), (n0 + n) % VFS_PAGE_SIZE, m) ]) subst: [ino, md, boolvar, m0, m3, m1, dirs, files0, files1, content1, content0, m, n, buf, n1, n0] → [ino, md, boolvar, m0, m4, m1, dirs, files0, files1, content, content0, min(n1 - n0 + n, n2), n, buf, n1, n0] flags: <all paths>

Additional information

Used terms: ino, md, boolvar, m0, m4, m1, dirs, files0, files1, content, content0, min(n1 - n0 + n, n2), n, buf, n1, n0