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Proof step 13 from proof inv-renam (previous step)

files[dirs[m4].entries[str]] = mkfile(m5, md3, m9, content), new_child_inode = mkinode(m0, md0, boolvar, m1, m2, m3), new_parent_inode = mkinode(m, md, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size), old_child_inode = mkinode(dirs[m4].entries[str], md2, boolvar0, m6, m7, m8), old_dent = mkdentry(str, dirs[m4].entries[str]), old_parent_inode = mkinode(m4, md1, true, dirs[m4].nlink, dirs[m4].nsubdirs, dirs[m4].size), afs-cons(dirs, files), m ∈ dirs, str ∈ dirs[m4].entries, m4 ∈ dirs, m = m4 → md = md1, (links(m, dirs) ≠ ∅ ∨ m = ROOT_INO) ∧ ¬ new_dent.name ∈ dirs[m].entries ∧ new_dent.negdentry? ∨ (links(m, dirs) ≠ ∅ ∨ m = ROOT_INO) ∧ (new_dent.ino ∈ dirs ∨ new_dent.ino ∈ files) ∧ new_dent.name ∈ dirs[m].entries ∧ new_dent.ino = dirs[m].entries[new_dent.name] ∧ new_dent.dentry? ∧ ( new_dent.ino ∈ dirs ∧ m1 = dirs[new_dent.ino].nlink ∧ m3 = dirs[new_dent.ino].size ∧ m2 = dirs[new_dent.ino].nsubdirs ∧ boolvar ∨ new_dent.ino ∈ files ∧ m1 = files[new_dent.ino].nlink ∧ m2 = 0 ∧ ¬ boolvar) ∧ m0 = new_dent.ino ∧ (new_dent.ino ∈ files ↔ dirs[m4].entries[str] ∈ files) ∧ (new_dent.ino ∈ dirs → new_dent.ino ≠ ROOT_INO ∧ dirs[new_dent.ino].entries = ∅), dirs[m4].entries[str] ∈ dirs ∧ m6 = dirs[dirs[m4].entries[str]].nlink ∧ m8 = dirs[dirs[m4].entries[str]].size ∧ m7 = dirs[dirs[m4].entries[str]].nsubdirs ∧ boolvar0 ∨ dirs[m4].entries[str] ∈ files ∧ m6 = m9 ∧ m7 = 0 ∧ ¬ boolvar0, dirs[m4].entries[str] ∈ dirs ∨ dirs[m4].entries[str] ∈ files, links(m4, dirs) ≠ ∅ ∨ m4 = ROOT_INO ⊦ ⟪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 14:
files[dirs[m4].entries[str]] = mkfile(m5, md3, m9, content), files[new_dent.ino] = mkfile(m10, md4, m11, content0), new_child_inode = mkinode(m0, md0, boolvar, m1, m2, m3), new_parent_inode = mkinode(m, md, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size), old_child_inode = mkinode(dirs[m4].entries[str], md2, boolvar0, m6, m7, m8), old_dent = mkdentry(str, dirs[m4].entries[str]), old_parent_inode = mkinode(m4, md1, true, dirs[m4].nlink, dirs[m4].nsubdirs, dirs[m4].size), afs-cons(dirs, files), m4 ∈ dirs, str ∈ dirs[m4].entries, m ∈ dirs, m = m4 → md = md1, links(m4, dirs) ≠ ∅ ∨ m4 = ROOT_INO, dirs[m4].entries[str] ∈ dirs ∨ dirs[m4].entries[str] ∈ files, dirs[m4].entries[str] ∈ dirs ∧ m6 = dirs[dirs[m4].entries[str]].nlink ∧ m8 = dirs[dirs[m4].entries[str]].size ∧ m7 = dirs[dirs[m4].entries[str]].nsubdirs ∧ boolvar0 ∨ dirs[m4].entries[str] ∈ files ∧ m6 = m9 ∧ m7 = 0 ∧ ¬ boolvar0, (links(m, dirs) ≠ ∅ ∨ m = ROOT_INO) ∧ ¬ new_dent.name ∈ dirs[m].entries ∧ new_dent.negdentry? ∨ (links(m, dirs) ≠ ∅ ∨ m = ROOT_INO) ∧ (new_dent.ino ∈ dirs ∨ new_dent.ino ∈ files) ∧ new_dent.name ∈ dirs[m].entries ∧ new_dent.ino = dirs[m].entries[new_dent.name] ∧ new_dent.dentry? ∧ ( new_dent.ino ∈ dirs ∧ m1 = dirs[new_dent.ino].nlink ∧ m3 = dirs[new_dent.ino].size ∧ m2 = dirs[new_dent.ino].nsubdirs ∧ boolvar ∨ new_dent.ino ∈ files ∧ m1 = m11 ∧ m2 = 0 ∧ ¬ boolvar) ∧ m0 = new_dent.ino ∧ (new_dent.ino ∈ files ↔ dirs[m4].entries[str] ∈ files) ∧ (new_dent.ino ∈ dirs → new_dent.ino ≠ ROOT_INO ∧ dirs[new_dent.ino].entries = ∅) ⊦ ⟪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-file name: elim seq: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content) subst: [af, m, md, m0, content] → [files[new_dent.ino], m10, md4, m11, content0]

Additional information

Used simplifier rules: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content); (elim) Used terms: files[new_dent.ino], m10, md4, m11, content0