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Proof step 189 from proof inv-rmdir (previous step)

# links(entries[str], dirs0) = m1 + 1, dirs0[ino1] = mkdir(m0 + 1, md1, # links(ino1, dirs0), m + 1, entries), dirs0[entries[str]] = mkdir(0, md, m1 + 1, m4, ∅), dirs = dirs0[ino1, mkdir(m0, md1, # links(ino1, dirs0), m, entries -- str)][entries[str], mkdir(0, md, m1, m4, ∅)], err = ESUCCESS, entries[str] ≠ ROOT_INO, entries[str] ≠ ino1, dom of < ino0, afs-cons(dirs0[ino1, mkdir(m0, md1, # links(ino1, dirs0), m, entries -- str)][entries[str], mkdir(0, md, m1, m4, ∅)], files), afs-cons(dirs0, files), ispath(q, ROOT_INO, ino1, dirs0, files), of-cons(of, dirs0, files), pw(user, md1), px(user, md1), px-parent(user, q, ROOT_INO, dirs0, files), entries[str] ∈ dirs0, str ∈ entries, ino1 ∈ dirs0, links(ino1, dirs0) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ ⟪vfs_put_inode#(getinode(entries[str], dirs, files), of, asynced; err, dirs, files)⟫ (of-cons(of, dirs, files) ∧ afs-cons(dirs, files))

User applied rule insert program lemma

And obtained the following new goals

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, getinode(entries[str], dirs, files), files, dirs, err] flags: <all paths>

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));%⊦ getinode(ino, dirs, files) = (ino ∈ dirs ⊃ mkinode (ino, dirs[ino].meta, true, dirs[ino].nlink, dirs[ino].nsubdirs, dirs[ino].size) ;mkinode (ino, files[ino].meta, false, files[ino].nlink, 0, files[ino].size) ); (s)% ⊦ ino ∈ dirs[ino0, ad] ↔ ino ∈ dirs; (s)% ⊦ dirs[ino, ad][ino0] = (ino0 = ino ∧ ino ∈ dirs ⊃ ad;dirs[ino0]); (s)% ⊦ mkdir(m, md, m0, m1, entries).meta = md; (s)% ⊦ mkdir(m, md, m0, m1, entries).nlink = m0; (s)% ⊦ mkdir(m, md, m0, m1, entries).nsubdirs = m1; (s)% ⊦ mkdir(m, md, m0, m1, entries).size = m; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)%⊦ of-cons(of, dirs, files) ∧ afs-cons(dirs, files) ∧ ino ∈ dirs → ¬ is-open(ino, of); (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)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nlink = m0; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).size = m2; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nsubdirs = m1; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).directory ↔ boolvar; (s)