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Proof step 105 from proof refine-mkdir (previous step)

entries[str] ∈ dirs ↔ root[q + str '].dir?, dirs[ino1] = mkdir(# entries, md0, # links(ino1, dirs), m1, entries), root[q].dir?, root.dir?, dom of < ino0, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(q, ROOT_INO, ino1, dirs, files), of-cons(of, dirs, files), pw(user, md0), px(user, md0), px-parent(user, q, ROOT_INO, dirs, files), ino1 ∈ dirs, str ∈ entries, psynced → asynced, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ pre-mkdir(q + str ', md, EEXISTS, user, root, abs-files(files), abs-of(of)) ∧ ⟨err0 := EEXISTS; if err0 = ESUCCESS then root[q + str '] := dnode(md, ∅); psynced := ?⟩ (abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ EEXISTS = err0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 106:
⊦ ispath(p, ino, m, dirs, files) ∧ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) → (p + str ' ∈ tree ↔ m ∈ dirs ∧ str ∈ dirs[m].entries)
Proof step 107:
entries[str] ∈ dirs ↔ root[q + str '].dir?, dirs[ino1] = mkdir(# entries, md0, # links(ino1, dirs), m1, entries), root[q].dir?, root.dir?, dom of < ino0, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(q, ROOT_INO, ino1, dirs, files), of-cons(of, dirs, files), pw(user, md0), px(user, md0), px-parent(user, q, ROOT_INO, dirs, files), ino1 ∈ dirs, str ∈ entries, psynced → asynced, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ ⟨err0 := EEXISTS; if err0 = ESUCCESS then root[q + str '] := dnode(md, ∅); psynced := ?⟩ (abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ EEXISTS = err0)

Rule argument

Additional information

Used simplifier rules: path-in-last: ⊦ ispath(p, ino, m, dirs, files) ∧ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) → (p + str ' ∈ tree ↔ m ∈ dirs ∧ str ∈ dirs[m].entries);% ⊦ mkdir(m, md, m0, m1, entries).entries = entries; (s)%a: ⊦ (p + p0) + p1 = p + p0 + p1; from specification list[path]% ⊦ pre-mkdir(p, md, EEXISTS, user, root, fs, ofh) ↔ p ∈ root; (s)