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Proof step 10 from proof inv-link (previous step)

c_inode = mkinode(dirs[ino].entries[str], md0, false, files[dirs[ino].entries[str]].nlink, 0, m3), new_dent = negdentry(str0), p_inode = mkinode(m, md, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size), afs-cons(dirs, files), dirs[ino].entries[str] ∈ files, m ∈ dirs, str ∈ dirs[ino].entries, ino ∈ dirs, ¬ str0 ∈ dirs[m].entries, links(dirs[ino].entries[str], dirs) ≠ ∅ ∨ dirs[ino].entries[str] = ROOT_INO, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO, links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO ⊦ ⟪afs_link#(mkdentry(str, dirs[ino].entries[str]); p_inode, c_inode, 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 11:
files[dirs[ino].entries[str]] = mkfile(m0, md1, m1, content), c_inode = mkinode(dirs[ino].entries[str], md0, false, m1, 0, m3), new_dent = negdentry(str0), p_inode = mkinode(m, md, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size), afs-cons(dirs, files), ino ∈ dirs, str ∈ dirs[ino].entries, m ∈ dirs, dirs[ino].entries[str] ∈ files, links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO, links(dirs[ino].entries[str], dirs) ≠ ∅ ∨ dirs[ino].entries[str] = ROOT_INO ⊦ ⟪afs_link#(mkdentry(str, dirs[ino].entries[str]); p_inode, c_inode, new_dent, err, dirs, files; asynced)⟫ afs-cons(dirs, files), str0 ∈ dirs[m].entries

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[ino].entries[str]], m0, md1, m1, content]

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[ino].entries[str]], m0, md1, m1, content