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Proof step 175 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, abs(root, ROOT_INO)(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, psynced → asynced ⊦ # links(entries0[str], dirs) = count(⌜entries0[str]⌝ , root.fids), root[path].dir?, entries0[str] ∈ dirs, p0 + str ∈ links(⌜dirs[lookup(parent(p0 + str), ROOT_INO, dirs, files)].entries[(p0 + str).last]⌝ , root) ∧ mklink(lookup(parent(p0 + str), ROOT_INO, dirs, files), (p0 + str).last) = mklink(m1, str)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 176:
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, abs(root, ROOT_INO)(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, psynced → asynced ⊦ # links(entries0[str], dirs) = count(⌜entries0[str]⌝ , root.fids), root[path].dir?, entries0[str] ∈ dirs, p0 + str ' ∈ links(⌜entries0[str]⌝ , root)

Rule argument

Additional information

Used simplifier rules: ⊦ mkdir(m, md, m0, m1, entries).entries = entries; (s)% ⊦ (p + str ').last = str; (s)% ⊦ ispath(p, n, m, dirs, files) → lookup(p, n, dirs, files) = m; (s)%a: ⊦ (p + p0) + p1 = p + p0 + p1; from specification list[path]% ⊦ parent(p + str ') = p; (s)% ⊦ p + str = p + str '; (s)