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Proof step 188 from proof refine-readmeta (previous step)

dirs[m1] = mkdir(# entries0, md0, # links(m1, dirs), m7, entries0), files[entries0[str]] = mkfile(m0, md1, # links(entries0[str], dirs), content), dirs[lookup(parent(p), ROOT_INO, dirs, files)] = mkdir(m2, md, m3, m4, entries), root[p0].dir?, root.dir?, dom of < ino6, (_∃(λ ino1. abs|(root, ROOT_INO, p0, ino1) * abs(root[p0], ino1)))(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(path, ROOT_INO, entries0[str], dirs, files), ispath(p0, ROOT_INO, m1, dirs, files), of-cons(of, dirs, files), pr(user, md1), px-parent(user, path, ROOT_INO, dirs, files), m1 ∈ dirs, str ∈ entries0, ROOT_INO ∈ dirs, entries0[str] ∈ files, p0 ∈ root, psynced → asynced ⊦ # links(entries0[str], dirs) = count(⌜entries0[str]⌝ , root.fids), root[p0][str '] = fnode(⌜entries0[str]⌝ ), root[path].dir?, entries0[str] ∈ dirs

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 189:
dirs[m1] = mkdir(# entries0, md0, # links(m1, dirs), m7, entries0), files[entries0[str]] = mkfile(m0, md1, # links(entries0[str], dirs), content), dirs[lookup(parent(p), ROOT_INO, dirs, files)] = mkdir(m2, md, m3, m4, entries), ((abs|(root, ROOT_INO, p0, m1) * abs(root[p0], m1)))(dirs), root[p0].dir?, root.dir?, dom of < ino6, afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(path, ROOT_INO, entries0[str], dirs, files), ispath(p0, ROOT_INO, m1, dirs, files), of-cons(of, dirs, files), pr(user, md1), px-parent(user, path, ROOT_INO, dirs, files), m1 ∈ dirs, str ∈ entries0, ROOT_INO ∈ dirs, entries0[str] ∈ files, p0 ∈ root, psynced → asynced ⊦ # links(entries0[str], dirs) = count(⌜entries0[str]⌝ , root.fids), root[p0][str '] = fnode(⌜entries0[str]⌝ ), root[path].dir?, entries0[str] ∈ dirs

Rule argument

Additional information

Used simplifier rules: absc-path: ⊦ p ∈ tree ∧ ((abs|(tree, ino, p, ino0) * D))(dirs) ∧ ispath(p, ino, ino1, dirs, files) → ino0 = ino1; (forward) from specification vfs-abs%sep-com: ⊦ D * D0 = D0 * D; from specification heap-sep[dir-heap]%sep-ass: ⊦ (D * D0) * D1 = D * D0 * D1; from specification heap-sep[dir-heap]% ⊦ (_∃ nD)(dirs) ↔ (∃ ino. nD(ino)(dirs)); (s)