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Proof step 113 from proof inv-write_inode (previous step)

dcache[key].ino = dirs[key.ino].entries[key.name], key.name = dcache[key].name, (key.ino = m ⊃ mkdir(m0, md, # links(key.ino, dirs), m2, entries);dirs[key.ino]) = mkdir(m6, md2, m7, m8, entries0), icache[m] = mkientry(boolvar, mkinode(m1, md1, boolvar0, m3, m4, m5)), dirs[m] = mkdir(m0, md0, # links(m, dirs), m2, entries), key.dentry?, dcache[key].dentry?, afs-cons(dirs[m, mkdir(m0, md, # links(m, dirs), m2, entries)], files), afs-cons(dirs, files), synced(dirs, icache, pcache), m ∈ icache, m ∈ dirs, key ∈ dcache, key.ino ∈ dirs, key.name ∈ dirs[key.ino].entries, 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(key.ino, dirs) ≠ ∅ ∨ key.ino = ROOT_INO, dcache[key].ino ∈ dirs ∨ dcache[key].ino ∈ files ⊦ key.name ∈ entries0 ∧ dcache[key].ino = entries0[key.name]

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 114:
dcache[key].ino = dirs[m9].entries[str], (m9 = m ⊃ mkdir(m0, md, # links(m9, dirs), m2, entries);dirs[m9]) = mkdir(m6, md2, m7, m8, entries0), dirs[m] = mkdir(m0, md0, # links(m, dirs), m2, entries), icache[m] = mkientry(boolvar, mkinode(m1, md1, boolvar0, m3, m4, m5)), key = dentrykey(m9, str), str = dcache[key].name, dcache[key].dentry?, key.dentry?, afs-cons(dirs, files), afs-cons(dirs[m, mkdir(m0, md, # links(m, dirs), m2, entries)], files), synced(dirs, icache, pcache), str ∈ dirs[m9].entries, m9 ∈ dirs, key ∈ dcache, m ∈ dirs, m ∈ icache, 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?, dcache[key].ino ∈ dirs ∨ dcache[key].ino ∈ files, links(m9, dirs) ≠ ∅ ∨ m9 = ROOT_INO ⊦ str ∈ entries0 ∧ dcache[key].ino = entries0[str]

Rule argument

spec: key name: elim-03 seq: ⊦ key.dentry? → (m = key.ino ∧ str = key.name ↔ key = dentrykey(m, str)) subst: [key, m, str] → [key, m9, str]

Additional information

Used simplifier rules: ⊦ key.dentry? → (m = key.ino ∧ str = key.name ↔ key = dentrykey(m, str)); (elim) Used terms: key, m9, str