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Proof step 180 from proof inv-unlink (previous step)

# links(entries[str], dirs0) = m1 + 1, dirs0[ino1] = mkdir(m, md1, # links(ino1, dirs0), m2, entries), files0[entries[str]] = mkfile(m0, md, m1 + 1, content), dirs = dirs1[ino, dirs1[ino].meta:= inode.meta], dirs1 = dirs0[ino1, mkdir(m - 1, md1, # links(ino1, dirs0), m2, entries -- str)], files = files0[entries[str], mkfile(m0, md, m1, content)], ino = inode.ino, inode = mkinode(ino1, md1, true, # links(ino1, dirs0), m2, m), dom of < ino0, afs-cons(dirs0, files0), ispath(q, ROOT_INO, ino1, dirs0, files0), of-cons(of, dirs0, files0), pw(user, md1), px(user, md1), px-parent(user, q, ROOT_INO, dirs0, files0), str ∈ entries, entries[str] ∈ files0, ino1 ∈ dirs0, ino ∈ dirs1, 1 ≤ m, links(ino1, dirs0) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ [afs_inode_sync#(mkinode(entries[str], md, false, # links(entries[str], dirs0), 0, m0); dirs, files); inode := (ino1 ∈ dirs ⊃ mkinode(ino1, dirs[ino1].meta, true, dirs[ino1].nlink, dirs[ino1].nsubdirs, dirs[ino1].size) ;mkinode(ino1, files[ino1].meta, false, files[ino1].nlink, 0, files[ino1].size) ); c_inode := getinode(entries[str], dirs, files); err := ESUCCESS; asynced := ?] (afs-cons(dirs, files) → ⟪vfs_put_inode#(c_inode, of, asynced; err, dirs, files)⟫ (of-cons(of, dirs, files) ∧ afs-cons(dirs, files))), m = 0, entries[str] ∈ dirs0, ino ∈ files

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 181:
# links(entries[str], dirs0) = m1 + 1, files0[entries[str]] = mkfile(m0, md, m1 + 1, content), dirs0[ino1] = mkdir(m, md1, # links(ino1, dirs0), m2, entries), dirs = dirs0[ino1, mkdir(m - 1, md1, # links(ino1, dirs0), m2, entries -- str)], files = files0[entries[str], mkfile(m0, md, m1, content)], m ≠ 0, dom of < ino0, afs-cons(dirs0, files0), ispath(q, ROOT_INO, ino1, dirs0, files0), of-cons(of, dirs0, files0), pw(user, md1), px(user, md1), px-parent(user, q, ROOT_INO, dirs0, files0), entries[str] ∈ files0, str ∈ entries, ino1 ∈ dirs0, 1 ≤ m, ¬ entries[str] ∈ dirs0, links(ino1, dirs0) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ [afs_inode_sync#(mkinode(entries[str], md, false, # links(entries[str], dirs0), 0, m0); dirs, files); inode := (ino1 ∈ dirs ⊃ mkinode(ino1, dirs[ino1].meta, true, dirs[ino1].nlink, dirs[ino1].nsubdirs, dirs[ino1].size) ;mkinode(ino1, files[ino1].meta, false, files[ino1].nlink, 0, files[ino1].size) ); c_inode := getinode(entries[str], dirs, files); err := ESUCCESS; asynced := ?] (afs-cons(dirs, files) → ⟪vfs_put_inode#(c_inode, of, asynced; err, dirs, files)⟫ (of-cons(of, dirs, files) ∧ afs-cons(dirs, files)))

Rule argument

Additional information

Used simplifier rules: ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs → ¬ ino ∈ files; (s)% ⊦ ino ∈ files[ino0, af] ↔ ino ∈ files; (s)% ⊦ ino ∈ dirs[ino0, ad] ↔ ino ∈ dirs; (s)% ⊦ dirs[ino, ad][ino, ad0] = dirs[ino, ad0]; (s)%⊦ mkdir(m, md, m0, m1, entries).meta:= md0 = mkdir(m, md0, m0, m1, entries); (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).meta = md; (s)% ⊦ dirs[ino, ad][ino0] = (ino0 = ino ∧ ino ∈ dirs ⊃ ad;dirs[ino0]); (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)