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Proof step 40 from proof inv-lookup (previous step)

dirs[key.ino] = mkdir(m0, md0, m2, m3, entries0), 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 ⊦ key = dentrykey(p_ino, dent0.name), 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 ∈ entries0 ∧ dcache[dentrykey(p_ino, dent0.name), mkdentry(dent0.name, entries[dent0.name])][key].ino = entries0[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?

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 41:
dirs[p_ino] = mkdir(m, md, # links(p_ino, dirs), m1, entries), dirs[key.ino] = mkdir(m0, md0, m2, m3, entries0), afs-cons(dirs, files), dcache-cons(dcache, dirs, files), synced(dirs, icache, pcache), dent0.name ∈ entries, p_ino ∈ dirs, key ∈ dcache, asynced1 → synced(files, icache, pcache), links(p_ino, dirs) ≠ ∅ ∨ p_ino = ROOT_INO ⊦ dentrykey(p_ino, dent0.name) ∈ dcache, key.dentry? ∧ key.name = dcache[key].name ∧ key.ino ∈ dirs ∧ (links(key.ino, dirs) ≠ ∅ ∨ key.ino = ROOT_INO) ∧ (dcache[key].ino ∈ dirs ∨ dcache[key].ino ∈ files) ∧ dcache[key].name ∈ entries0 ∧ dcache[key].ino = entries0[dcache[key].name] ∧ dcache[key].dentry?

Rule argument

Additional information

Used simplifier rules: ⊦ key ∈ dcache ∧ ¬ key0 ∈ dcache → dcache[key0, dent][key] = dcache[key]; (s)% ⊦ key ≠ key0 → (key ∈ dcache[key0, dent] ↔ key ∈ dcache); (s)