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Proof step 225 from proof refine-readmeta (previous step)

dirs[m1] = mkdir(m5, md0, m6, m7, entries0), files[m] = mkfile(m0, md1, # links(m, dirs), content), dirs[lookup(parent(p), ROOT_INO, dirs, files)] = mkdir(m2, md, m3, m4, entries), root[q1 + str '] = fnode(⌜m⌝ ), root[q0 + str '] = fnode(⌜m⌝ ), root[q1].dir?, root.dir?, root[q0].dir?, dom of < ino6, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(q1, ROOT_INO, m10, dirs, files), ispath(q0, ROOT_INO, m10, dirs, files), ispath(path, ROOT_INO, m, dirs, files), ispath(q0 + str ', ROOT_INO, m9, dirs, files), of-cons(of, dirs, files), pr(user, md1), px-parent(user, path, ROOT_INO, dirs, files), dirs[m10].entries[str] ∈ files, str ' ∈ root[q1], str ∈ dirs[m10].entries, ROOT_INO ∈ dirs, m ∈ files, str ' ∈ root[q0], m10 ∈ dirs, psynced → asynced ⊦ # links(m, dirs) = count(⌜m⌝ , root.fids), # links(⌜m⌝ , root) = 0, links(⌜m⌝ , root) = ∅, q0 = q1, root[path].dir?, m ∈ dirs, dirs[m10].entries[str] ∈ dirs, m9 ∈ dirs

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 226:
root[q0 + str '] = fnode(⌜m⌝ ), root[q1 + str '] = fnode(⌜m⌝ ), dirs[lookup(parent(p), ROOT_INO, dirs, files)] = mkdir(m2, md, m3, m4, entries), files[m] = mkfile(m0, md1, # links(m, dirs), content), dirs[m1] = mkdir(m5, md0, m6, m7, entries0), dirs[m10] = mkdir(m8, md2, m11, m12, entries1), root[q0].dir?, root.dir?, root[q1].dir?, dom of < ino6, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(q0 + str ', ROOT_INO, m9, dirs, files), ispath(path, ROOT_INO, m, dirs, files), ispath(q0, ROOT_INO, m10, dirs, files), ispath(q1, ROOT_INO, m10, dirs, files), of-cons(of, dirs, files), pr(user, md1), px-parent(user, path, ROOT_INO, dirs, files), m10 ∈ dirs, str ' ∈ root[q0], m ∈ files, ROOT_INO ∈ dirs, str ∈ entries1, str ' ∈ root[q1], entries1[str] ∈ files, psynced → asynced ⊦ # links(⌜m⌝ , root) = 0, # links(m, dirs) = count(⌜m⌝ , root.fids), links(⌜m⌝ , root) = ∅, q0 = q1, root[path].dir?, m9 ∈ dirs, entries1[str] ∈ dirs, m ∈ dirs

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[m10], m8, md2, m11, m12, entries1]

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[m10], m8, md2, m11, m12, entries1