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Proof step 7 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 ⊦ afs-cons (dirs, files1 [ino, mkfile (m1, md1, 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))]) ]) ∧ ino ∈ files0 ∧ m = m1 ∧ m2 = m1 ∧ md0 = md1 ∧ files1 -- ino = files0 -- ino ∧ n0 + n + min(n1 - n0 + n, n2) ≤ n1 ∧ n1 ≤ # buf + n0 ∧ 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 cut formula

And obtained the following new goals

Proof step 8:
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), 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))]), ino ∈ files1, (n0 + n) % VFS_PAGE_SIZE + min(n1 - n0 + n, n2) ≤ VFS_PAGE_SIZE ⊦ afs-cons (dirs, files1 [ino, mkfile (m1, md1, 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))]) ]) ∧ ino ∈ files0 ∧ m = m1 ∧ m2 = m1 ∧ md0 = md1 ∧ files1 -- ino = files0 -- ino ∧ n0 + n + min(n1 - n0 + n, n2) ≤ n1 ∧ n1 ≤ # buf + n0 ∧ 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))])
Proof step 25:
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))]), afs-cons (dirs, files1 [ino, mkfile (m1, md1, 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))]) ]) ∧ ino ∈ files0 ∧ m = m1 ∧ m2 = m1 ∧ md0 = md1 ∧ files1 -- ino = files0 -- ino ∧ n0 + n + min(n1 - n0 + n, n2) ≤ n1 ∧ n1 ≤ # buf + n0 ∧ 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))])

Rule argument

fma: 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)) ])

Additional information

Used formulas: 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)) ])