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Proof step 95 from proof inv-create (previous step)

# links(ino0, dirs0) = m0, dirs0[ino0] = mkdir(m, md0, # links(ino0, dirs0), m1, entries), dirs0[p_ino, dirs0[p_ino].entries:= dirs0[p_ino].entries[dent.name, ino]][p_ino] = mkdir(m2, md1, m3, m4, entries0), dent = negdentry(str), dirs = dirs0[p_ino, dirs0[p_ino].entries:= dirs0[p_ino].entries[dent.name, ino]] [p_ino, dirs0[p_ino, dirs0[p_ino].entries:= dirs0[p_ino].entries[dent.name, ino]][p_ino].size:= (m2 + 1) ], err = ESUCCESS, files = (files0 ++ ino)[ino, mkfile(0, md, 1, ∅)], p_ino = ino0, afs-cons(dirs0, files0), ispath(q, ROOT_INO, ino0, dirs0, files0), of-cons(of, dirs0, files0), pw(user, md0), px(user, md0), px-parent(user, q, ROOT_INO, dirs0, files0), ino0 ∈ dirs0, links(ino0, dirs0) ≠ ∅ ∨ ino0 = ROOT_INO ⊦ [afs_inode_sync#(mkinode(ino0, md0, true, m0, m1, m); dirs, files); inode := (ino0 ∈ dirs ⊃ mkinode(ino0, dirs[ino0].meta, true, dirs[ino0].nlink, dirs[ino0].nsubdirs, dirs[ino0].size) ;mkinode(ino0, files[ino0].meta, false, files[ino0].nlink, 0, files[ino0].size) ); c_inode := getinode(mkdentry(dent.name, ino).ino, dirs, files); asynced := ?] (afs-cons(dirs, files) → of-cons(of, dirs, files)), ino = 0, str ∈ entries, ino ∈ files0, ino ∈ dirs0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 96:
dirs0[ino0] = mkdir(m2, md1, # links(ino0, dirs0), m4, entries), dirs = dirs0[ino0, mkdir(m2 + 1, md1, # links(ino0, dirs0), m4, entries[str, ino])], files = (files0 ++ ino)[ino, mkfile(0, md, 1, ∅)], ino ≠ 0, afs-cons(dirs0, files0), ispath(q, ROOT_INO, ino0, dirs0, files0), of-cons(of, dirs0, files0), pw(user, md1), px(user, md1), px-parent(user, q, ROOT_INO, dirs0, files0), ino0 ∈ dirs0, ¬ ino ∈ dirs0, ¬ ino ∈ files0, ¬ str ∈ entries, links(ino0, dirs0) ≠ ∅ ∨ ino0 = ROOT_INO ⊦ [afs_inode_sync#(mkinode(ino0, md1, true, # links(ino0, dirs0), m4, m2); dirs, files); inode := (ino0 ∈ dirs ⊃ mkinode(ino0, dirs[ino0].meta, true, dirs[ino0].nlink, dirs[ino0].nsubdirs, dirs[ino0].size) ;mkinode(ino0, files[ino0].meta, false, files[ino0].nlink, 0, files[ino0].size) ); c_inode := getinode(mkdentry(str, ino).ino, dirs, files); asynced := ?] (afs-cons(dirs, files) → of-cons(of, dirs, files))

Rule argument

Additional information

Used simplifier rules: ⊦ mkdir(m, md, m0, m1, entries).size:= m2 = mkdir(m2, md, m0, m1, entries); (s)%⊦ mkdir(m, md, m0, m1, entries) = mkdir(m2, md0, m3, m4, entries0) ↔ m = m2 ∧ md = md0 ∧ m0 = m3 ∧ m1 = m4 ∧ entries = entries0; (ws)%⊦ mkdir(m, md, m0, m1, entries).entries:= entries0 = mkdir(m, md, m0, m1, entries0); (s)% ⊦ mkdir(m, md, m0, m1, entries).entries = entries; (s)% ⊦ dirs[ino, ad][ino, ad0] = dirs[ino, ad0]; (s)% ⊦ dirs[ino, ad][ino0] = (ino0 = ino ∧ ino ∈ dirs ⊃ ad;dirs[ino0]); (s)% ⊦ negdentry(str).name = str; (s)