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Proof step 249 from proof inv-write (previous step)

# links(m, dirs) = files[m].nlink, m1 + n1 = m1 / VFS_PAGE_SIZE * VFS_PAGE_SIZE + VFS_PAGE_SIZE, files1[m] = mkfile(m1, md0, files[m].nlink, content0), of[fd] = mkfile(m, mode, m0), m1 = n2 + m1 / VFS_PAGE_SIZE * VFS_PAGE_SIZE, m1 < m0 + ino4, dom of < ino3, afs-cons(dirs, files1), afs-cons(dirs, files), of-cons(of, dirs, files1), of-cons(of, dirs, files), m ∈ files, fd ∈ of, m1 / VFS_PAGE_SIZE ∈ content0, m ∈ files1, n2 + n1 ≤ VFS_PAGE_SIZE, n ≤ # buf0, m1 % VFS_PAGE_SIZE + n1 ≤ VFS_PAGE_SIZE ⊦ ino4 = 0, n = 0, n2 = 0, mode ≠ MODE_W ∧ mode ≠ MODE_RW, err1 = ESUCCESS ∧ ¬ isdir, of-cons(of[fd, mkfile(m, mode, m0 + ino4)], dirs, files[m, (files[m].meta:= md0).size:= (m0 + ino4)]) ∧ afs-cons(dirs, files[m, (files[m].meta:= md0).size:= (m0 + ino4)])

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 250:
# links(m, dirs) = m3, m1 + n1 = m1 / VFS_PAGE_SIZE * VFS_PAGE_SIZE + VFS_PAGE_SIZE, of[fd] = mkfile(m, mode, m0), files1[m] = mkfile(m1, md0, m3, content0), files[m] = mkfile(m2, md, m3, content), m1 = n2 + m1 / VFS_PAGE_SIZE * VFS_PAGE_SIZE, dom of < ino3, m1 < m0 + ino4, afs-cons(dirs, files), afs-cons(dirs, files1), of-cons(of, dirs, files), of-cons(of, dirs, files1), m ∈ files1, m1 / VFS_PAGE_SIZE ∈ content0, fd ∈ of, m ∈ files, m1 % VFS_PAGE_SIZE + n1 ≤ VFS_PAGE_SIZE, n ≤ # buf0, n2 + n1 ≤ VFS_PAGE_SIZE ⊦ ino4 = 0, n = 0, n2 = 0, of-cons(of[fd, mkfile(m, mode, m0 + ino4)], dirs, files[m, (files[m].meta:= md0).size:= (m0 + ino4)]) ∧ afs-cons(dirs, files[m, (files[m].meta:= md0).size:= (m0 + ino4)]), err1 = ESUCCESS ∧ ¬ isdir, mode ≠ MODE_W ∧ mode ≠ MODE_RW

Rule argument

spec: abstract-file name: elim seq: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content) subst: [af, m, md, m0, content] → [files[m], m2, md, m3, content]

Additional information

Used simplifier rules: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content); (elim) Used terms: files[m], m2, md, m3, content