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Proof step 23 from proof inv-close (previous step)

of[fd] = mkfile(m, mode, m0), files[m] = mkfile(m1, md, m2, content), err = ESUCCESS, dom of < ino0, afs-cons(dirs, files), of-cons(of, dirs, files), fd ∈ of ⊦ ⟪vfs_put_inode#(mkinode(m, md, false, m2, 0, m1), of -- fd, asynced; err, dirs, files)⟫ (of-cons(of -- fd, dirs, files) ∧ afs-cons(dirs, files))

User applied rule insert program lemma

And obtained the following new goals

Proof step 24:
afs-cons(dirs, files), of-cons(of, dirs, files), ¬ is-open(inode.ino, of) → pre-evict(inode, dirs, files) ⊦ ⟪vfs_put_inode#(inode, of, asynced; err, dirs, files)⟫ (afs-cons(dirs, files) ∧ of-cons(of, dirs, files))
Proof step 25:
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))

Rule argument

spec: <toplevel> name: inv-put-inode seq: afs-cons(dirs, files), of-cons(of, dirs, files), ¬ is-open(inode.ino, of) → pre-evict(inode, dirs, files) ⊦ ⟪vfs_put_inode#(inode, of, asynced; err, dirs, files)⟫ (afs-cons(dirs, files) ∧ of-cons(of, dirs, files)) subst: [asynced, of, inode, files, dirs, err] → [asynced, of -- fd, mkinode(m, md, false, m2, 0, m1), files, dirs, err] flags: <all paths>

Additional information

Used simplifier rules: ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)%⊦ pre-evict(inode, dirs, files) ↔ valid-wb-inode(inode, dirs, files) ∧ inode.ino ≠ ROOT_INO; (s)%⊦ valid-wb-inode(inode, dirs, files) ↔ valid-dir-inode(inode, dirs, files) ∨ valid-file-inode(inode, dirs, files); (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-dir-ino(ino, dirs, files) ↔ ino ∈ dirs; (s)%⊦ of-cons(of, dirs, files) ∧ fd ∈ of ∧ of[fd] = mkfile(ino, mode, n) ∧ afs-cons(dirs, files) → ¬ ino ∈ dirs; (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)% ⊦ valid-file-ino(ino, dirs, files) ↔ ino ∈ files; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nlink = m0; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nsubdirs = m1; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).directory ↔ boolvar; (s)