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Proof step 132 from proof refine-writemeta (previous step)

(ino1 ∈ dirs ⊃ mkinode(ino1, dirs[ino1].meta, true, dirs[ino1].nlink, dirs[ino1].nsubdirs, dirs[ino1].size) ;mkinode(ino1, files[ino1].meta, false, files[ino1].nlink, 0, files[ino1].size) ) = mkinode(m, md0, boolvar, m0, m1, m2), root[path].dir? ↔ ino1 ∈ dirs, files[m] = mkfile(m3, md, m4, content), root.dir?, dom of < ino0, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(path, ROOT_INO, ino1, dirs, files), of-cons(of, dirs, files), pw(user, md0), px-parent(user, path, ROOT_INO, dirs, files), psynced → asynced0, ino1 ∈ dirs ∨ ino1 ∈ files ⊦ m ∈ files ∧ m0 = m4 ∧ m1 = 0 ∧ ¬ boolvar, m ∈ dirs ∧ m0 = dirs[m].nlink ∧ m2 = dirs[m].size ∧ m1 = dirs[m].nsubdirs ∧ boolvar

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 133:
(ino1 ∈ dirs ⊃ mkinode(ino1, dirs[ino1].meta, true, dirs[ino1].nlink, dirs[ino1].nsubdirs, dirs[ino1].size) ;mkinode(ino1, files[ino1].meta, false, files[ino1].nlink, 0, files[ino1].size) ) = mkinode(m, md0, boolvar, m0, m1, m2), root[path].dir? ↔ ino1 ∈ dirs, files[m] = mkfile(m3, md, m4, content), dirs[m] = mkdir(m5, md1, m6, m7, entries), root.dir?, dom of < ino0, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(path, ROOT_INO, ino1, dirs, files), of-cons(of, dirs, files), pw(user, md0), px-parent(user, path, ROOT_INO, dirs, files), psynced → asynced0, ino1 ∈ dirs ∨ ino1 ∈ files ⊦ m ∈ dirs ∧ m0 = m6 ∧ m2 = m5 ∧ m1 = m7 ∧ boolvar, m ∈ files ∧ m0 = m4 ∧ m1 = 0 ∧ ¬ boolvar

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[m], m5, md1, m6, m7, entries]

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[m], m5, md1, m6, m7, entries