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Proof step 118 from proof inv-write_inode (previous step)

(m9 = m ⊃ mkdir(m0, md, # links(m, dirs), m2, entries);dirs[m9]) = mkdir(m6, md2, m7, m8, entries0), dcache[dentrykey(m9, str)] = mkdentry(str, entries1[str]), icache[m] = mkientry(boolvar, mkinode(m1, md1, boolvar0, m3, m4, m5)), dirs[m] = mkdir(m0, md0, # links(m, dirs), m2, entries), dirs[m9] = mkdir(m10, md3, m11, m12, entries1), 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, dentrykey(m9, str) ∈ dcache, m9 ∈ 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(m9, dirs) ≠ ∅ ∨ m9 = ROOT_INO, entries1[str] ∈ dirs ∨ entries1[str] ∈ files ⊦ str ∈ entries0 ∧ entries1[str] = entries0[str]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 119:
(m9 = m ⊃ mkdir(m0, md, # links(m, dirs), m2, entries);mkdir(m10, md3, # links(m9, dirs), m12, entries1)) = mkdir(m6, md2, m7, m8, entries0), dcache[dentrykey(m9, str)] = mkdentry(str, entries1[str]), icache[m] = mkientry(boolvar, mkinode(m1, md1, boolvar0, m3, m4, m5)), dirs[m] = mkdir(m0, md0, # links(m, dirs), m2, entries), dirs[m9] = mkdir(m10, md3, # links(m9, dirs), m12, entries1), 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, dentrykey(m9, str) ∈ dcache, m9 ∈ 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(m9, dirs) ≠ ∅ ∨ m9 = ROOT_INO, entries1[str] ∈ dirs ∨ entries1[str] ∈ files ⊦ str ∈ entries0 ∧ entries1[str] = entries0[str]

Rule argument

Additional information

Used simplifier rules: afs-cons-dir-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs ∧ dirs[ino] = mkdir(n0, md, n, n1, entries) → # links(ino, dirs) = n; (forward) from specification afs-base