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Proof step 330 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, false, files[m5].nlink, 0, m8), 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, ∅), fs = abs-files(files), entries0 ≠ ∅, m1 ≠ 0, m2 ≠ 0, m5 ≠ ROOT_INO, root.dir?, root[q].dir?, dom of < ino0, abs(root, ROOT_INO)(dirs0), afs-cons(dirs0, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(q, ROOT_INO, ino1, dirs0, files), of-cons(of, dirs0, files), pw(user, md2), px(user, md2), px-parent(user, q, ROOT_INO, dirs0, files), m5 ∈ 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, ¬ is-open(m5, of), ¬ m5 ∈ dirs, psynced → asynced0, links(ino1, dirs0) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ [if files[m5].nlink = 0 then files := files -- m5] ( of-cons(of, dirs, files) ∧ afs-cons(dirs, files) → ⟨posix_rmdir#(q + str ', user, fs, abs-of(of); err1, root; psynced)⟩ (fs = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ ESUCCESS = err1))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 331:
# 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, false, m7, 0, m8), 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), files[m5] = mkfile(m6, md4, m7, content), fs = abs-files(files), root[q].dir?, root.dir?, dom of < ino0, abs(root, ROOT_INO)(dirs0), afs-cons(dirs0, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(q, ROOT_INO, ino1, dirs0, files), of-cons(of, dirs0, 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, m5 ∈ files, 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 ⊦ [if m7 = 0 then files := files -- m5] ( of-cons(of, dirs, files) ∧ afs-cons(dirs, files) → ⟨posix_rmdir#(q + str ', user, fs, abs-of(of); err1, root; psynced)⟩ (fs = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ ESUCCESS = err1)), entries0 = ∅, m1 = 0, m2 = 0, m5 = ROOT_INO, is-open(m5, of), m5 ∈ dirs

Rule argument

spec: abstract-file name: elim seq: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content) subst: [af, m, md, m0, content] → [files[m5], m6, md4, m7, content]

Additional information

Used simplifier rules: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content); (elim) Used terms: files[m5], m6, md4, m7, content