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Proof step 25 from proof refine-renam (previous step)

# links(m, cache_dirs) = m5, # links(m3, cache_dirs) = m20, cache_dirs[entries0[str]] = mkdir(m0, md7, m1, m2, entries1), cache_dirs[m3] = mkdir(m19, md5, # links(m3, cache_dirs), m21, entries), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries0[str]] = mkfile(m15, md3, m16, content), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[negdentry(str0).ino] = mkfile(m17, md4, m18, content0), cache_dirs[m] = mkdir(m4, md6, # links(m, cache_dirs), m6, entries0), cache_dirs[negdentry(str0).ino] = mkdir(m11, md8, m22, m23, entries2), afs_dirs = cache_dirs, afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, err = err0, new_child_inode = mkinode(m7, md1, boolvar, m8, m9, m10), new_dent = negdentry(str0), new_parent_inode = mkinode(m3, md0, true, # links(m3, cache_dirs), m21, m19), old_child_inode = mkinode(entries0[str], md2, boolvar0, m12, m13, m14), old_dent = mkdentry(str, entries0[str]), old_parent_inode = mkinode(m, md, true, # links(m, cache_dirs), m6, m4), afs-cons(cache_dirs, cache_files), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), dcache-cons(cache_dcache, cache_dirs, cache_files), icache-cons(cache_icache, cache_dirs, cache_files), pcache-cons(cache_pcache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache), m3 ∈ cache_dirs, str ∈ entries0, m ∈ cache_dirs, ¬ str0 ∈ entries, m3 = m → md0 = md, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m3, cache_dirs) ≠ ∅ ∨ m3 = ROOT_INO, entries0[str] ∈ cache_dirs ∧ m12 = m1 ∧ m14 = m0 ∧ m13 = m2 ∧ boolvar0 ∨ entries0[str] ∈ cache_files ∧ m12 = m16 ∧ m13 = 0 ∧ ¬ boolvar0, entries0[str] ∈ cache_dirs ∨ entries0[str] ∈ cache_files, links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪cache_rename# (; old_parent_inode, new_parent_inode, old_child_inode, new_child_inode, old_dent, new_dent, err, cache_dirs, cache_files, cache_icache, cache_dcache, cache_asynced)⟫ ⟨old_dent0 := mkdentry(str, entries0[str]); p_inode := mkinode(m, md, true, m5, m6, m4); p_inode0 := mkinode(m3, md0, true, m20, m21, m19); p_inode2 := mkinode(m7, md1, boolvar, m8, m9, m10); p_inode1 := mkinode(entries0[str], md2, boolvar0, m12, m13, m14); old_dent1 := negdentry(str0); afs_rename#(; p_inode, p_inode0, p_inode1, p_inode2, old_dent0, old_dent1, err0, afs_dirs, afs_files; afs_asynced)⟩ ( afs_dirs = cache_dirs ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ cache_asynced) ∧ old_parent_inode = p_inode ∧ new_parent_inode = p_inode0 ∧ old_child_inode = p_inode1 ∧ new_child_inode = p_inode2 ∧ old_dent = old_dent0 ∧ new_dent = old_dent1 ∧ err = err0)

User applied rule cut formula

And obtained the following new goals

Proof step 26:
# links(m3, cache_dirs) = m20, # links(m, cache_dirs) = m5, cache_dirs[negdentry(str0).ino] = mkdir(m11, md8, m22, m23, entries2), cache_dirs[m] = mkdir(m4, md6, # links(m, cache_dirs), m6, entries0), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[negdentry(str0).ino] = mkfile(m17, md4, m18, content0), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries0[str]] = mkfile(m15, md3, m16, content), cache_dirs[m3] = mkdir(m19, md5, # links(m3, cache_dirs), m21, entries), cache_dirs[entries0[str]] = mkdir(m0, md7, m1, m2, entries1), afs_dirs = cache_dirs, afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, err = err0, new_child_inode = mkinode(m7, md1, boolvar, m8, m9, m10), new_dent = negdentry(str0), new_parent_inode = mkinode(m3, md0, true, # links(m3, cache_dirs), m21, m19), old_child_inode = mkinode(entries0[str], md2, boolvar0, m12, m13, m14), old_dent = mkdentry(str, entries0[str]), old_parent_inode = mkinode(m, md, true, # links(m, cache_dirs), m6, m4), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), afs-cons(cache_dirs, cache_files), dcache-cons(cache_dcache, cache_dirs, cache_files), icache-cons(cache_icache, cache_dirs, cache_files), pcache-cons(cache_pcache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache), m ∈ cache_dirs, str ∈ entries0, m3 ∈ cache_dirs, old_child_inode.ino ∈ cache_dirs, cache_sync → synced(cache_files, cache_icache, cache_pcache), m3 = m → md0 = md, links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO, entries0[str] ∈ cache_dirs ∨ entries0[str] ∈ cache_files, entries0[str] ∈ cache_dirs ∧ m12 = m1 ∧ m14 = m0 ∧ m13 = m2 ∧ boolvar0 ∨ entries0[str] ∈ cache_files ∧ m12 = m16 ∧ m13 = 0 ∧ ¬ boolvar0, links(m3, cache_dirs) ≠ ∅ ∨ m3 = ROOT_INO ⊦ ⟪cache_rename# (; old_parent_inode, new_parent_inode, old_child_inode, new_child_inode, old_dent, new_dent, err, cache_dirs, cache_files, cache_icache, cache_dcache, cache_asynced)⟫ ⟨old_dent0 := mkdentry(str, entries0[str]); p_inode := mkinode(m, md, true, m5, m6, m4); p_inode0 := mkinode(m3, md0, true, m20, m21, m19); p_inode2 := mkinode(m7, md1, boolvar, m8, m9, m10); p_inode1 := mkinode(entries0[str], md2, boolvar0, m12, m13, m14); old_dent1 := negdentry(str0); afs_rename#(; p_inode, p_inode0, p_inode1, p_inode2, old_dent0, old_dent1, err0, afs_dirs, afs_files; afs_asynced)⟩ ( afs_dirs = cache_dirs ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ cache_asynced) ∧ old_parent_inode = p_inode ∧ new_parent_inode = p_inode0 ∧ old_child_inode = p_inode1 ∧ new_child_inode = p_inode2 ∧ old_dent = old_dent0 ∧ new_dent = old_dent1 ∧ err = err0), str0 ∈ entries
Proof step 52:
# links(m3, cache_dirs) = m20, # links(m, cache_dirs) = m5, cache_dirs[negdentry(str0).ino] = mkdir(m11, md8, m22, m23, entries2), cache_dirs[m] = mkdir(m4, md6, # links(m, cache_dirs), m6, entries0), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[negdentry(str0).ino] = mkfile(m17, md4, m18, content0), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries0[str]] = mkfile(m15, md3, m16, content), cache_dirs[m3] = mkdir(m19, md5, # links(m3, cache_dirs), m21, entries), cache_dirs[entries0[str]] = mkdir(m0, md7, m1, m2, entries1), afs_dirs = cache_dirs, afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, err = err0, new_child_inode = mkinode(m7, md1, boolvar, m8, m9, m10), new_dent = negdentry(str0), new_parent_inode = mkinode(m3, md0, true, # links(m3, cache_dirs), m21, m19), old_child_inode = mkinode(entries0[str], md2, boolvar0, m12, m13, m14), old_dent = mkdentry(str, entries0[str]), old_parent_inode = mkinode(m, md, true, # links(m, cache_dirs), m6, m4), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), afs-cons(cache_dirs, cache_files), dcache-cons(cache_dcache, cache_dirs, cache_files), icache-cons(cache_icache, cache_dirs, cache_files), pcache-cons(cache_pcache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache), m ∈ cache_dirs, str ∈ entries0, m3 ∈ cache_dirs, cache_sync → synced(cache_files, cache_icache, cache_pcache), m3 = m → md0 = md, links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO, entries0[str] ∈ cache_dirs ∨ entries0[str] ∈ cache_files, entries0[str] ∈ cache_dirs ∧ m12 = m1 ∧ m14 = m0 ∧ m13 = m2 ∧ boolvar0 ∨ entries0[str] ∈ cache_files ∧ m12 = m16 ∧ m13 = 0 ∧ ¬ boolvar0, links(m3, cache_dirs) ≠ ∅ ∨ m3 = ROOT_INO ⊦ ⟪cache_rename# (; old_parent_inode, new_parent_inode, old_child_inode, new_child_inode, old_dent, new_dent, err, cache_dirs, cache_files, cache_icache, cache_dcache, cache_asynced)⟫ ⟨old_dent0 := mkdentry(str, entries0[str]); p_inode := mkinode(m, md, true, m5, m6, m4); p_inode0 := mkinode(m3, md0, true, m20, m21, m19); p_inode2 := mkinode(m7, md1, boolvar, m8, m9, m10); p_inode1 := mkinode(entries0[str], md2, boolvar0, m12, m13, m14); old_dent1 := negdentry(str0); afs_rename#(; p_inode, p_inode0, p_inode1, p_inode2, old_dent0, old_dent1, err0, afs_dirs, afs_files; afs_asynced)⟩ ( afs_dirs = cache_dirs ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ cache_asynced) ∧ old_parent_inode = p_inode ∧ new_parent_inode = p_inode0 ∧ old_child_inode = p_inode1 ∧ new_child_inode = p_inode2 ∧ old_dent = old_dent0 ∧ new_dent = old_dent1 ∧ err = err0), old_child_inode.ino ∈ cache_dirs, str0 ∈ entries

Rule argument

fma: old_child_inode.ino ∈ cache_dirs

Additional information

Used formulas: old_child_inode.ino ∈ cache_dirs