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Proof step 37 from proof inv-lookup (previous step)

dirs[p_ino] = mkdir(m, md, # links(p_ino, dirs), m1, entries), afs-cons(dirs, files), dcache-cons(dcache, dirs, files), synced(dirs, icache, pcache), dent0.name ∈ entries, p_ino ∈ dirs, asynced1 → synced(files, icache, pcache), links(p_ino, dirs) ≠ ∅ ∨ p_ino = ROOT_INO ⊦ dentrykey(p_ino, dent0.name) ∈ dcache, ∀ key. key ∈ dcache[dentrykey(p_ino, dent0.name), mkdentry(dent0.name, entries[dent0.name])] → key.dentry? ∧ key.name = dcache[dentrykey(p_ino, dent0.name), mkdentry(dent0.name, entries[dent0.name])][key].name ∧ valid-dentry(key.ino, dcache[dentrykey(p_ino, dent0.name), mkdentry(dent0.name, entries[dent0.name])][key], dirs, files)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 38:
dirs[p_ino] = mkdir(m, md, # links(p_ino, dirs), m1, entries), afs-cons(dirs, files), dcache-cons(dcache, dirs, files), synced(dirs, icache, pcache), key ∈ dcache[dentrykey(p_ino, dent0.name), mkdentry(dent0.name, entries[dent0.name])], p_ino ∈ dirs, dent0.name ∈ entries, asynced1 → synced(files, icache, pcache), links(p_ino, dirs) ≠ ∅ ∨ p_ino = ROOT_INO ⊦ dentrykey(p_ino, dent0.name) ∈ dcache, key.dentry? ∧ key.name = dcache[dentrykey(p_ino, dent0.name), mkdentry(dent0.name, entries[dent0.name])][key].name ∧ key.ino ∈ dirs ∧ (links(key.ino, dirs) ≠ ∅ ∨ key.ino = ROOT_INO) ∧ ( dcache[dentrykey(p_ino, dent0.name), mkdentry(dent0.name, entries[dent0.name])][key].ino ∈ dirs ∨ dcache[dentrykey(p_ino, dent0.name), mkdentry(dent0.name, entries[dent0.name])][key].ino ∈ files) ∧ dcache[dentrykey(p_ino, dent0.name), mkdentry(dent0.name, entries[dent0.name])][key].name ∈ dirs[key.ino].entries ∧ dcache[dentrykey(p_ino, dent0.name), mkdentry(dent0.name, entries[dent0.name])][key].ino = dirs[key.ino].entries[dcache[dentrykey(p_ino, dent0.name), mkdentry(dent0.name, entries[dent0.name])][key].name] ∧ dcache[dentrykey(p_ino, dent0.name), mkdentry(dent0.name, entries[dent0.name])][key].dentry?

Rule argument

Additional information

Used simplifier rules: ⊦ valid-ino(ino, dirs, files) ↔ ino ∈ dirs ∨ ino ∈ files; (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)