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Proof step 363 from proof refine-rmdir (previous step)

# entries0 = m + 1, (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) ) = mkinode(m5, md3, boolvar, m6, m7, m8), dirs0[ino1] = mkdir(m + 1, md2, # links(ino1, dirs0), m2, entries0), root[q] = dnode(md2, sdt), dirs1[entries0[str]] = mkdir(m0, md0, m1, m4, entries), dirs0[entries0[str]] = mkdir(0, md, # links(entries0[str], dirs0), m3, ∅), root[q + str '] = dnode(md1, ∅), (( abs(sdt[str], entries0[str]) * abs(sdt -- str, entries0 -- str) * ino1 => mkdir(m, md2, # links(ino1, dirs0), m2 - 1, entries0 -- str) * abs|(root, ROOT_INO, q, ino1)) )(dirs1), root.dir?, dom of < ino0, afs-cons(dirs, files), afs-cons(dirs0, files), fids-cons(root, abs-files(files), abs-of(of)), is-open(m5, 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), str ∈ sdt, entries0[str] ∈ dirs3, ino1 ∈ dirs2, str ∈ entries0, entries0[str] ∈ dirs0, entries0[str] ∈ dirs1, q ∈ root, ino1 ∈ dirs0, 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, psynced0 → asynced0, links(ino1, dirs0) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ entries0 = ∅, m1 = 0, m2 = 0, abs(root -- (q + str '), ROOT_INO)(dirs)

Heuristic if-then-else split applied rule case distinction

And closed the goal!

Rule argument

pos: left 2

Additional information

Used simplifier rules: ⊦ mkinode(m, md, boolvar, m0, m1, m2) = mkinode(m3, md0, boolvar0, m4, m5, m6) ↔ m = m3 ∧ md = md0 ∧ (boolvar ↔ boolvar0) ∧ m0 = m4 ∧ m1 = m5 ∧ m2 = m6; (ws)%⊦ of-cons(of, dirs, files) ∧ afs-cons(dirs, files) ∧ ino ∈ dirs → ¬ is-open(ino, of); (s)