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Proof step 35 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), p_ino ∈ dirs, dent0.name ∈ entries, asynced1 → synced(files, icache, pcache), links(p_ino, dirs) ≠ ∅ ∨ p_ino = ROOT_INO ⊦ dcache-cons(dcache[dentrykey(p_ino, dent0.name), mkdentry(dent0.name, entries[dent0.name])], dirs, files), dentrykey(p_ino, dent0.name) ∈ dcache

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 36:
⊦ dcache-cons(dcache, dirs, files) ↔ (∀ key. key ∈ dcache → key.dentry? ∧ key.name = dcache[key].name ∧ valid-dentry(key.ino, dcache[key], dirs, files))
Proof step 37:
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)

Rule argument

spec: cache-base name: dcache-cons seq: ⊦ dcache-cons(dcache, dirs, files) ↔ (∀ key. key ∈ dcache → key.dentry? ∧ key.name = dcache[key].name ∧ valid-dentry(key.ino, dcache[key], dirs, files)) subst: [dcache, dirs, files] → [dcache [dentrykey(p_ino, dent0.name), mkdentry(dent0.name, entries[dent0.name]) ], dirs, files] flags: <all paths>

Additional information

Used terms: dcache [dentrykey(p_ino, dent0.name), mkdentry(dent0.name, entries[dent0.name]) ], dirs, files