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Proof step 197 from proof inv-write_inode (previous step)

(m5 = m ⊃ mkdir(m0, md, # links(m, dirs), m2, entries);dirs[m5]) = mkdir(m1, md1, m3, m4, entries0), dirs[m] = mkdir(m0, md0, # links(m, dirs), m2, entries), dcache[dentrykey(m5, str)] = mkdentry(str, dirs[m5].entries[str]), afs-cons(dirs[m, mkdir(m0, md, # links(m, dirs), m2, entries)], files), afs-cons(dirs, files), synced(dirs, icache, pcache), str ∈ dirs[m5].entries, m5 ∈ dirs, dentrykey(m5, str) ∈ dcache, m ∈ dirs, asynced2 → synced(files, icache, pcache), ∀ key0. key0 ∈ dcache → key0.dentry? ∧ key0.name = dcache[key0].name ∧ key0.ino ∈ dirs ∧ (links(key0.ino, dirs) ≠ ∅ ∨ key0.ino = ROOT_INO) ∧ (dcache[key0].ino ∈ dirs ∨ dcache[key0].ino ∈ files) ∧ dcache[key0].name ∈ dirs[key0.ino].entries ∧ dcache[key0].ino = dirs[key0.ino].entries[dcache[key0].name] ∧ dcache[key0].dentry?, dirs[m5].entries[str] ∈ dirs ∨ dirs[m5].entries[str] ∈ files, links(m5, dirs) ≠ ∅ ∨ m5 = ROOT_INO ⊦ m ∈ icache, str ∈ entries0 ∧ dirs[m5].entries[str] = entries0[str]

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 198:
(m5 = m ⊃ mkdir(m0, md, # links(m, dirs), m2, entries);dirs[m5]) = mkdir(m1, md1, m3, m4, entries0), dcache[dentrykey(m5, str)] = mkdentry(str, entries1[str]), dirs[m] = mkdir(m0, md0, # links(m, dirs), m2, entries), dirs[m5] = mkdir(m6, md2, m7, m8, entries1), afs-cons(dirs, files), afs-cons(dirs[m, mkdir(m0, md, # links(m, dirs), m2, entries)], files), synced(dirs, icache, pcache), m ∈ dirs, dentrykey(m5, str) ∈ dcache, m5 ∈ dirs, str ∈ entries1, asynced2 → synced(files, icache, pcache), ∀ key0. key0 ∈ dcache → key0.dentry? ∧ key0.name = dcache[key0].name ∧ key0.ino ∈ dirs ∧ (links(key0.ino, dirs) ≠ ∅ ∨ key0.ino = ROOT_INO) ∧ (dcache[key0].ino ∈ dirs ∨ dcache[key0].ino ∈ files) ∧ dcache[key0].name ∈ dirs[key0.ino].entries ∧ dcache[key0].ino = dirs[key0.ino].entries[dcache[key0].name] ∧ dcache[key0].dentry?, links(m5, dirs) ≠ ∅ ∨ m5 = ROOT_INO, entries1[str] ∈ dirs ∨ entries1[str] ∈ files ⊦ m ∈ icache, str ∈ entries0 ∧ entries1[str] = entries0[str]

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[m5], m6, md2, m7, m8, entries1]

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[m5], m6, md2, m7, m8, entries1