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Proof step 40 from proof write-block-inv (previous step)

# getpage((n0 + n2) / VFS_PAGE_SIZE, content) = VFS_PAGE_SIZE, VFS_PAGE_SIZE = n3 + (n0 + n2) % VFS_PAGE_SIZE, files1[m] = mkfile(m3, md0, m4, content), write-inv(n0, n1, mkinode(m, md, boolvar, m0, m1, m2), buf1, n2, dirs, files0, files1), m ∈ files1, n2 + min(n1 - n0 + n2, n3) ≤ # buf1, (n0 + n2) % VFS_PAGE_SIZE + min(n1 - n0 + n2, n3) ≤ VFS_PAGE_SIZE, n0 + n2 ≤ n1 ⊦ min(n1 - n0 + n2, n3) = 0, write-inv (n0, n1, mkinode(m, md, boolvar, m0, m1, m2), buf1, n2 + min(n1 - n0 + n2, n3), dirs, files0, files1 [m, mkfile (m3, md0, m4, content[(n0 + n2) / VFS_PAGE_SIZE, copy(buf1, n2, getpage((n0 + n2) / VFS_PAGE_SIZE, content), (n0 + n2) % VFS_PAGE_SIZE, min(n1 - n0 + n2, n3))]) ])

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: write-inv-strong-rec seq: ino ∈ files1, files1[ino] = mkfile(m2, md0, m3, content), (n0 + n) % VFS_PAGE_SIZE + min(n1 - n0 + n, n2) ≤ VFS_PAGE_SIZE, write-inv (n0, n1, mkinode(ino, md, boolvar, m0, m4, m1), buf, n, dirs, files0, files1) ⊦ write-inv (n0, n1, mkinode(ino, md, boolvar, m0, m4, m1), buf, n + min(n1 - n0 + n, n2), dirs, files0, files1 [ino, mkfile (m2, md0, m3, 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)) ]) ]) subst: [content, m3, md0, m2, files1, files0, dirs, n2, n, buf, m1, m4, m0, boolvar, md, ino, n1, n0] → [content, m4, md0, m3, files1, files0, dirs, n3, n2, buf1, m2, m1, m0, boolvar, md, m, n1, n0] flags: <all paths>

Additional information

Used terms: content, m4, md0, m3, files1, files0, dirs, n3, n2, buf1, m2, m1, m0, boolvar, md, m, n1, n0