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Proof step 25 from proof inv-close (previous step)

files[m] = mkfile(m1, md, m2, content), of[fd] = mkfile(m, mode, m0), err = ESUCCESS, dom of < ino0, afs-cons(dirs, files), of-cons(of, dirs, files), fd ∈ of ⊦ afs-cons(dirs, files) ∧ of-cons(of -- fd, dirs, files) ∧ (¬ is-open(mkinode(m, md, false, m2, 0, m1).ino, of -- fd) → pre-evict(mkinode(m, md, false, m2, 0, m1), dirs, files))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 26:
⊦ of-cons(of0, dirs0, files0) → (of-cons(of1, dirs1, files1) ↔ (∀ n. (n ∈ of0 → of0[n].ino ∈ files0) → n ∈ of1 → of1[n].ino ∈ files1))
Proof step 27:
of[fd] = mkfile(ROOT_INO, mode, m0), files[ROOT_INO] = mkfile(m1, md, m2, content), dom of < ino0, afs-cons(dirs, files), of-cons(of -- fd, dirs, files), of-cons(of, dirs, files), fd ∈ of ⊦ is-open(ROOT_INO, of -- fd)

Rule argument

Additional information

Used simplifier rules: of-cons-reduce: ⊦ of-cons(of0, dirs0, files0) → ( of-cons(of1, dirs1, files1) ↔ (∀ n. (n ∈ of0 → of0[n].ino ∈ files0) → n ∈ of1 → of1[n].ino ∈ files1));% ⊦ fd ≠ fd0 → (of -- fd0)[fd] = of[fd]; (s)% ⊦ fd ∈ of -- fd0 ↔ fd ≠ fd0 ∧ fd ∈ of; (s)% ⊦ mkfile(m, md, m0, content).nlink = m0; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).directory ↔ boolvar; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nsubdirs = m1; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nlink = m0; (s)%⊦ of-cons(of, dirs, files) ∧ fd ∈ of ∧ of[fd] = mkfile(ino, mode, n) → ino ∈ files; (ss)% ⊦ valid-file-ino(ino, dirs, files) ↔ ino ∈ files; (s)%⊦ valid-file-inode(inode, dirs, files) ↔ valid-file-ino(inode.ino, dirs, files) ∧ inode.nlink = files[inode.ino].nlink ∧ inode.nsubdirs = 0 ∧ ¬ inode.directory; (s)%⊦ of-cons(of, dirs, files) ∧ fd ∈ of ∧ of[fd] = mkfile(ino, mode, n) ∧ afs-cons(dirs, files) → ¬ ino ∈ dirs; (s)% ⊦ valid-dir-ino(ino, dirs, files) ↔ ino ∈ dirs; (s)%⊦ valid-dir-inode(inode, dirs, files) ↔ valid-dir-ino(inode.ino, dirs, files) ∧ inode.nlink = dirs[inode.ino].nlink ∧ inode.size = dirs[inode.ino].size ∧ inode.nsubdirs = dirs[inode.ino].nsubdirs ∧ inode.directory; (s)%⊦ valid-wb-inode(inode, dirs, files) ↔ valid-dir-inode(inode, dirs, files) ∨ valid-file-inode(inode, dirs, files); (s)%⊦ pre-evict(inode, dirs, files) ↔ valid-wb-inode(inode, dirs, files) ∧ inode.ino ≠ ROOT_INO; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)