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Proof step 344 from proof refine-rmdir (previous step)

# entries0 = m + 1, dirs1[entries0[str]] = mkdir(m0, md0, m1, m4, entries), dirs0[entries0[str]] = mkdir(0, md, # links(entries0[str], dirs0), m3, ∅), dirs0[ino1] = mkdir(m + 1, md2, # links(ino1, dirs0), m2, entries0), root[q + str '] = dnode(md1, ∅), err = ESUCCESS, fs = abs-files(files), p_inode = getinode(entries0[str], dirs, files), root.dir?, root[q].dir?, dom of < ino0, abs(root, ROOT_INO)(dirs0), afs-cons(dirs, files), afs-cons(dirs0, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(q, ROOT_INO, ino1, dirs0, files), of-cons(of, dirs, files), of-cons(of, dirs0, files), pw(user, md2), px(user, md2), px-parent(user, q, ROOT_INO, dirs0, files), entries0[str] ∈ dirs3, ino1 ∈ dirs2, str ∈ entries0, ino1 ∈ dirs0, entries0[str] ∈ dirs0, entries0[str] ∈ dirs1, dirs2 ≡ dirs1[entries0[str], mkdir(m0, md0, m1 - 1, m4, entries)], dirs1 ≡ dirs0[ino1, mkdir(m, md2, # links(ino1, dirs0), m2 - 1, entries0 -- str)], dirs3 ≡ dirs2[ino1, dirs2[ino1].meta:= md2], dirs ≡ dirs3[entries0[str], dirs3[entries0[str]].meta:= md], 1 ≤ m1, 1 ≤ m2, psynced → asynced0, links(ino1, dirs0) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ ⟨posix_rmdir#(q + str ', user, fs, abs-of(of); err1, root; psynced)⟩ (fs = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ err = err1), entries0 = ∅, m1 = 0, m2 = 0, err = ESUCCESS ∧ ¬ is-open(p_inode.ino, of)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 345:
# entries0 = m + 1, root[q + str '] = dnode(md1, ∅), dirs0[ino1] = mkdir(m + 1, md2, # links(ino1, dirs0), m2, entries0), dirs0[entries0[str]] = mkdir(0, md, # links(entries0[str], dirs0), m3, ∅), dirs1[entries0[str]] = mkdir(m0, md0, m1, m4, entries), entries0 ≠ ∅, m1 ≠ 0, m2 ≠ 0, root[q].dir?, root.dir?, dom of < ino0, abs(root, ROOT_INO)(dirs0), afs-cons(dirs0, files), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), is-open ((entries0[str] ∈ dirs ⊃ mkinode(entries0[str], dirs[entries0[str]].meta, true, dirs[entries0[str]].nlink, dirs[entries0[str]].nsubdirs, dirs[entries0[str]].size) ;mkinode(entries0[str], files[entries0[str]].meta, false, files[entries0[str]].nlink, 0, files[entries0[str]].size) ) .ino, of), ispath(q, ROOT_INO, ino1, dirs0, files), of-cons(of, dirs0, files), of-cons(of, dirs, files), pw(user, md2), px(user, md2), px-parent(user, q, ROOT_INO, dirs0, files), entries0[str] ∈ dirs1, entries0[str] ∈ dirs0, ino1 ∈ dirs0, str ∈ entries0, ino1 ∈ dirs2, entries0[str] ∈ dirs3, dirs ≡ dirs3[entries0[str], dirs3[entries0[str]].meta:= md], dirs3 ≡ dirs2[ino1, dirs2[ino1].meta:= md2], dirs1 ≡ dirs0[ino1, mkdir(m, md2, # links(ino1, dirs0), m2 - 1, entries0 -- str)], dirs2 ≡ dirs1[entries0[str], mkdir(m0, md0, m1 - 1, m4, entries)], 1 ≤ m2, 1 ≤ m1, psynced → asynced0, links(ino1, dirs0) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ ⟨posix_rmdir#(q + str ', user, abs-files(files), abs-of(of); err1, root; psynced)⟩ (abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ ESUCCESS = err1)

Rule argument

Additional information

Used simplifier rules: ⊦ getinode(ino, dirs, files) = (ino ∈ dirs ⊃ mkinode (ino, dirs[ino].meta, true, dirs[ino].nlink, dirs[ino].nsubdirs, dirs[ino].size) ;mkinode (ino, files[ino].meta, false, files[ino].nlink, 0, files[ino].size) ); (s)