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Proof step 21 from proof inv-rename-negdentry (previous step)

dirs[entries0[str]] = mkdir(m9, md5, m11, m12, entries1), dirs[m] = mkdir(m6, md3, # links(m, dirs), m8, entries), files[entries0[str]] = mkfile(m1, md2, m5, content), dirs[m0] = mkdir(m7, md4, # links(m0, dirs), m10, entries0), new_dent = negdentry(str0), new_parent_inode = mkinode(m, md, true, # links(m, dirs), m8, m6), old_child_inode = mkinode(entries0[str], md1, boolvar, m2, m3, m4), old_dent = mkdentry(str, entries0[str]), old_parent_inode = mkinode(m0, md0, true, # links(m0, dirs), m10, m7), afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), m ∈ dirs, m0 ∈ dirs, str ∈ entries0, ¬ str0 ∈ entries, asynced → synced(files, icache, pcache), m = m0 → md = md0, entries0[str] ∈ dirs ∧ m2 = m11 ∧ m4 = m9 ∧ m3 = m12 ∧ boolvar ∨ entries0[str] ∈ files ∧ m2 = m5 ∧ m3 = 0 ∧ ¬ boolvar, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO, links(m0, dirs) ≠ ∅ ∨ m0 = ROOT_INO, entries0[str] ∈ dirs ∨ entries0[str] ∈ files ⊦ ⟪cache_rename# (; old_parent_inode, new_parent_inode, old_child_inode, new_child_inode, old_dent, new_dent, err, dirs, files, icache, dcache, asynced0)⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ afs-cons(dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced → synced(files, icache, pcache)))

User applied rule cut formula

And obtained the following new goals

Proof step 22:
dirs[m0] = mkdir(m7, md4, # links(m0, dirs), m10, entries0), files[entries0[str]] = mkfile(m1, md2, m5, content), dirs[m] = mkdir(m6, md3, # links(m, dirs), m8, entries), dirs[entries0[str]] = mkdir(m9, md5, m11, m12, entries1), new_dent = negdentry(str0), new_parent_inode = mkinode(m, md, true, # links(m, dirs), m8, m6), old_child_inode = mkinode(entries0[str], md1, boolvar, m2, m3, m4), old_dent = mkdentry(str, entries0[str]), old_parent_inode = mkinode(m0, md0, true, # links(m0, dirs), m10, m7), old_child_inode.directory, afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), str ∈ entries0, m0 ∈ dirs, m ∈ dirs, m = m0 → md = md0, asynced → synced(files, icache, pcache), entries0[str] ∈ dirs ∨ entries0[str] ∈ files, links(m0, dirs) ≠ ∅ ∨ m0 = ROOT_INO, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO, entries0[str] ∈ dirs ∧ m2 = m11 ∧ m4 = m9 ∧ m3 = m12 ∧ boolvar ∨ entries0[str] ∈ files ∧ m2 = m5 ∧ m3 = 0 ∧ ¬ boolvar ⊦ ⟪cache_rename# (; old_parent_inode, new_parent_inode, old_child_inode, new_child_inode, old_dent, new_dent, err, dirs, files, icache, dcache, asynced0)⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ afs-cons(dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced → synced(files, icache, pcache))), str0 ∈ entries
Proof step 25:
dirs[m0] = mkdir(m7, md4, # links(m0, dirs), m10, entries0), files[entries0[str]] = mkfile(m1, md2, m5, content), dirs[m] = mkdir(m6, md3, # links(m, dirs), m8, entries), dirs[entries0[str]] = mkdir(m9, md5, m11, m12, entries1), new_dent = negdentry(str0), new_parent_inode = mkinode(m, md, true, # links(m, dirs), m8, m6), old_child_inode = mkinode(entries0[str], md1, boolvar, m2, m3, m4), old_dent = mkdentry(str, entries0[str]), old_parent_inode = mkinode(m0, md0, true, # links(m0, dirs), m10, m7), afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), str ∈ entries0, m0 ∈ dirs, m ∈ dirs, m = m0 → md = md0, asynced → synced(files, icache, pcache), entries0[str] ∈ dirs ∨ entries0[str] ∈ files, links(m0, dirs) ≠ ∅ ∨ m0 = ROOT_INO, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO, entries0[str] ∈ dirs ∧ m2 = m11 ∧ m4 = m9 ∧ m3 = m12 ∧ boolvar ∨ entries0[str] ∈ files ∧ m2 = m5 ∧ m3 = 0 ∧ ¬ boolvar ⊦ ⟪cache_rename# (; old_parent_inode, new_parent_inode, old_child_inode, new_child_inode, old_dent, new_dent, err, dirs, files, icache, dcache, asynced0)⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ afs-cons(dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced → synced(files, icache, pcache))), old_child_inode.directory, str0 ∈ entries

Rule argument

fma: old_child_inode.directory

Additional information

Used formulas: old_child_inode.directory