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Proof step 491 from proof inv-rename-file-dentry (previous step)

dirs0[m3] = mkdir(m1, md1, # links(m3, dirs0), m4, entries), files[entries[str0]] = mkfile(m0, md0, # links(entries[str0], dirs0), content), afs-cons(dirs0, files), afs-cons (dirs0[m3, mkdir(m1, md2, # links(m3, dirs0), m4, entries)], files[entries[str0], mkfile(m, md3, # links(entries[str0], dirs0), content)]), dcache-cons(dcache0, dirs0, files), synced(dirs0, icache0, pcache), m3 ∈ dirs0, str0 ∈ entries, entries[str0] ∈ files, asynced2 → synced(files, icache0, pcache), links(m3, dirs0) ≠ ∅ ∨ m3 = ROOT_INO ⊦ entries[str0] ∈ dirs0, ∀ key. key ∈ dcache0[dentrykey(m3, str0), mkdentry(str0, entries[str0])] → key.dentry? ∧ key.name = dcache0[dentrykey(m3, str0), mkdentry(str0, entries[str0])][key].name ∧ valid-dentry (key.ino, dcache0[dentrykey(m3, str0), mkdentry(str0, entries[str0])][key], dirs0[m3, mkdir(m1, md2, # links(m3, dirs0), m4, entries)], files[entries[str0], mkfile(m, md3, # links(entries[str0], dirs0), content)])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 492:
files[entries[str0]] = mkfile(m0, md0, # links(entries[str0], dirs0), content), dirs0[m3] = mkdir(m1, md1, # links(m3, dirs0), m4, entries), afs-cons (dirs0[m3, mkdir(m1, md2, # links(m3, dirs0), m4, entries)], files[entries[str0], mkfile(m, md3, # links(entries[str0], dirs0), content)]), afs-cons(dirs0, files), dcache-cons(dcache0, dirs0, files), synced(dirs0, icache0, pcache), key ∈ dcache0[dentrykey(m3, str0), mkdentry(str0, entries[str0])], entries[str0] ∈ files, str0 ∈ entries, m3 ∈ dirs0, asynced2 → synced(files, icache0, pcache), links(m3, dirs0) ≠ ∅ ∨ m3 = ROOT_INO ⊦ entries[str0] ∈ dirs0, key.dentry? ∧ key.name = dcache0[dentrykey(m3, str0), mkdentry(str0, entries[str0])][key].name ∧ key.ino ∈ dirs0 ∧ (links(key.ino, dirs0) ≠ ∅ ∨ key.ino = ROOT_INO) ∧ ( dcache0[dentrykey(m3, str0), mkdentry(str0, entries[str0])][key].ino ∈ dirs0 ∨ dcache0[dentrykey(m3, str0), mkdentry(str0, entries[str0])][key].ino ∈ files) ∧ dcache0[dentrykey(m3, str0), mkdentry(str0, entries[str0])][key].name ∈ (key.ino = m3 ⊃ mkdir(m1, md2, # links(key.ino, dirs0), m4, entries);dirs0[key.ino]).entries ∧ dcache0[dentrykey(m3, str0), mkdentry(str0, entries[str0])][key].ino = (key.ino = m3 ⊃ mkdir(m1, md2, # links(key.ino, dirs0), m4, entries);dirs0[key.ino]).entries [dcache0[dentrykey(m3, str0), mkdentry(str0, entries[str0])][key].name ] ∧ dcache0[dentrykey(m3, str0), mkdentry(str0, entries[str0])][key].dentry?

Rule argument

Additional information

Used simplifier rules: ⊦ dirs[ino, ad][ino0] = (ino0 = ino ∧ ino ∈ dirs ⊃ ad;dirs[ino0]); (s)% ⊦ ino ∈ files[ino0, af] ↔ ino ∈ files; (s)% ⊦ valid-ino(ino, dirs, files) ↔ ino ∈ dirs ∨ ino ∈ files; (s)%⊦ ino ∈ dirs ∧ dirs[ino] = mkdir(m0, md0, n1, n2, entries) → links(ino0, dirs[ino, mkdir(m, md, n, n0, entries)]) = links(ino0, dirs); (s)% ⊦ ino ∈ dirs[ino0, ad] ↔ ino ∈ dirs; (s)%⊦ valid-parent-ino(ino, dirs, files) ↔ ino ∈ dirs ∧ (links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO); (s)%⊦ valid-dentry(ino, dent, dirs, files) ↔ valid-parent-ino(ino, dirs, files) ∧ valid-ino(dent.ino, dirs, files) ∧ dent.name ∈ dirs[ino].entries ∧ dent.ino = dirs[ino].entries[dent.name] ∧ dent.dentry?; (s)