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Proof step 27 from proof inv-lookup (previous step)

err = ESUCCESS, afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), dent.name ∈ dirs[p_ino].entries, p_ino ∈ dirs, ¬ dentrykey(p_ino, dent.name) ∈ dcache, asynced1 → synced(files, icache, pcache), links(p_ino, dirs) ≠ ∅ ∨ p_ino = ROOT_INO ⊦ ⟪dcache_set#(p_ino, dent.name, mkdentry(dent.name, dirs[p_ino].entries[dent.name]); err, dcache)⟫ dcache-cons(dcache, dirs, files)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 28:
dirs[p_ino] = mkdir(m, md, m0, m1, entries), err = ESUCCESS, afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), p_ino ∈ dirs, dent.name ∈ entries, asynced1 → synced(files, icache, pcache), links(p_ino, dirs) ≠ ∅ ∨ p_ino = ROOT_INO ⊦ ⟪dcache_set#(p_ino, dent.name, mkdentry(dent.name, entries[dent.name]); err, dcache)⟫ dcache-cons(dcache, dirs, files), dentrykey(p_ino, dent.name) ∈ dcache

Rule argument

spec: abstract-dir name: elim seq: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries) subst: [ad, m, md, m0, m1, entries] → [dirs[p_ino], m, md, m0, m1, entries]

Additional information

Used simplifier rules: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries); (elim) Used terms: dirs[p_ino], m, md, m0, m1, entries