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Proof step 16 from proof afs-cons-rename-dentry (previous step)

dirs[m].entries[str] ∈ files ↔ dirs[m0].entries[str0] ∈ files, files[dirs[m].entries[str]] = mkfile(m1, md3, m8, content), new_child_inode = mkinode(dirs[m].entries[str], md1, boolvar, m2, m3, m4), new_dent = mkdentry(str, dirs[m].entries[str]), new_parent_inode = mkinode(m, md, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size), 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 ∈ dirs[m].entries, m = m0 → md = md0, dirs[m].entries[str] ∈ dirs → dirs[m].entries[str] ≠ ROOT_INO ∧ dirs[dirs[m].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 ∨ dirs[m0].entries[str0] ∈ files ∧ m5 = files[dirs[m0].entries[str0]].nlink ∧ m6 = 0 ∧ ¬ boolvar0, dirs[m].entries[str] ∈ dirs ∧ m2 = dirs[dirs[m].entries[str]].nlink ∧ m4 = dirs[dirs[m].entries[str]].size ∧ m3 = dirs[dirs[m].entries[str]].nsubdirs ∧ boolvar ∨ dirs[m0].entries[str0] ∈ files ∧ m2 = m8 ∧ m3 = 0 ∧ ¬ boolvar, links(m0, dirs) ≠ ∅ ∨ m0 = ROOT_INO, dirs[m0].entries[str0] ∈ dirs ∨ dirs[m0].entries[str0] ∈ files, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO, dirs[m].entries[str] ∈ dirs ∨ dirs[m0].entries[str0] ∈ 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 17:
dirs[m].entries[str] ∈ files ↔ dirs[m0].entries[str0] ∈ files, files[dirs[m].entries[str]] = mkfile(m1, md3, m8, content), files[dirs[m0].entries[str0]] = mkfile(m9, md4, m10, content0), new_child_inode = mkinode(dirs[m].entries[str], md1, boolvar, m2, m3, m4), new_dent = mkdentry(str, dirs[m].entries[str]), new_parent_inode = mkinode(m, md, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size), 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), str ∈ dirs[m].entries, str0 ∈ dirs[m0].entries, m ∈ dirs, m0 ∈ dirs, dirs[m].entries[str] ∈ dirs → dirs[m].entries[str] ≠ ROOT_INO ∧ dirs[dirs[m].entries[str]].entries = ∅, m = m0 → md = md0, dirs[m].entries[str] ∈ dirs ∨ dirs[m0].entries[str0] ∈ files, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO, dirs[m0].entries[str0] ∈ dirs ∨ dirs[m0].entries[str0] ∈ files, links(m0, dirs) ≠ ∅ ∨ m0 = ROOT_INO, dirs[m].entries[str] ∈ dirs ∧ m2 = dirs[dirs[m].entries[str]].nlink ∧ m4 = dirs[dirs[m].entries[str]].size ∧ m3 = dirs[dirs[m].entries[str]].nsubdirs ∧ boolvar ∨ dirs[m0].entries[str0] ∈ files ∧ m2 = m8 ∧ m3 = 0 ∧ ¬ boolvar, 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 ∨ dirs[m0].entries[str0] ∈ 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-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[dirs[m0].entries[str0]], m9, md4, m10, 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[dirs[m0].entries[str0]], m9, md4, m10, content0