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Proof step 19 from proof afs-cons-rename-dentry (previous step)

entries[str] ∈ files ↔ dirs[m0].entries[str0] ∈ files, files[dirs[m0].entries[str0]] = mkfile(m9, md4, m10, content0), files[entries[str]] = mkfile(m1, md3, m8, content), dirs[m] = mkdir(m11, md5, # links(m, dirs), m13, entries), new_child_inode = mkinode(entries[str], md1, boolvar, m2, m3, m4), new_dent = mkdentry(str, entries[str]), new_parent_inode = mkinode(m, md, true, # links(m, dirs), m13, m11), old_child_inode = mkinode(dirs[m0].entries[str0], md2, boolvar0, m5, m6, m7), old_dent = mkdentry(str0, dirs[m0].entries[str0]), old_parent_inode = mkinode(m0, md0, true, dirs[m0].nlink, dirs[m0].nsubdirs, dirs[m0].size), afs-cons(dirs, files), m0 ∈ dirs, m ∈ dirs, str0 ∈ dirs[m0].entries, str ∈ entries, m = m0 → md = md0, entries[str] ∈ dirs → entries[str] ≠ ROOT_INO ∧ dirs[entries[str]].entries = ∅, dirs[m0].entries[str0] ∈ dirs ∧ m5 = dirs[dirs[m0].entries[str0]].nlink ∧ m7 = dirs[dirs[m0].entries[str0]].size ∧ m6 = dirs[dirs[m0].entries[str0]].nsubdirs ∧ boolvar0 ∨ entries[str] ∈ files ∧ m5 = m10 ∧ m6 = 0 ∧ ¬ boolvar0, entries[str] ∈ dirs ∧ m2 = dirs[entries[str]].nlink ∧ m4 = dirs[entries[str]].size ∧ m3 = dirs[entries[str]].nsubdirs ∧ boolvar ∨ entries[str] ∈ files ∧ m2 = m8 ∧ m3 = 0 ∧ ¬ boolvar, links(m0, dirs) ≠ ∅ ∨ m0 = ROOT_INO, dirs[m0].entries[str0] ∈ dirs ∨ entries[str] ∈ files, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO, entries[str] ∈ dirs ∨ entries[str] ∈ files ⊦ ⟪afs_rename#(; old_parent_inode, new_parent_inode, old_child_inode, new_child_inode, old_dent, new_dent, err, dirs, files; asynced)⟫ afs-cons(dirs, files)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 20:
entries[str] ∈ files ↔ entries0[str0] ∈ files, dirs[m] = mkdir(m11, md5, # links(m, dirs), m13, entries), files[entries[str]] = mkfile(m1, md3, m8, content), files[entries0[str0]] = mkfile(m9, md4, m10, content0), dirs[m0] = mkdir(m12, md6, m14, m15, entries0), new_child_inode = mkinode(entries[str], md1, boolvar, m2, m3, m4), new_dent = mkdentry(str, entries[str]), new_parent_inode = mkinode(m, md, true, # links(m, dirs), m13, m11), old_child_inode = mkinode(entries0[str0], md2, boolvar0, m5, m6, m7), old_dent = mkdentry(str0, entries0[str0]), old_parent_inode = mkinode(m0, md0, true, m14, m15, m12), afs-cons(dirs, files), str ∈ entries, str0 ∈ entries0, m ∈ dirs, m0 ∈ dirs, entries[str] ∈ dirs → entries[str] ≠ ROOT_INO ∧ dirs[entries[str]].entries = ∅, m = m0 → md = md0, entries[str] ∈ dirs ∨ entries[str] ∈ files, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO, entries0[str0] ∈ dirs ∨ entries[str] ∈ files, links(m0, dirs) ≠ ∅ ∨ m0 = ROOT_INO, entries[str] ∈ dirs ∧ m2 = dirs[entries[str]].nlink ∧ m4 = dirs[entries[str]].size ∧ m3 = dirs[entries[str]].nsubdirs ∧ boolvar ∨ entries[str] ∈ files ∧ m2 = m8 ∧ m3 = 0 ∧ ¬ boolvar, entries0[str0] ∈ dirs ∧ m5 = dirs[entries0[str0]].nlink ∧ m7 = dirs[entries0[str0]].size ∧ m6 = dirs[entries0[str0]].nsubdirs ∧ boolvar0 ∨ entries[str] ∈ files ∧ m5 = m10 ∧ m6 = 0 ∧ ¬ boolvar0 ⊦ ⟪afs_rename#(; old_parent_inode, new_parent_inode, old_child_inode, new_child_inode, old_dent, new_dent, err, dirs, files; asynced)⟫ afs-cons(dirs, files)

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[m0], m12, md6, m14, m15, entries0]

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[m0], m12, md6, m14, m15, entries0