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Proof step 287 from proof afs-cons-rename-file-dentry (previous step)

# links(m, dirs) = dirs[m].nlink, # links(m0, dirs) = dirs[m0].nlink, # links(entries[str], dirs) = files[entries[str]].nlink, entries0[str0] = dirs[m0].entries[str0], entries[str] = dirs[m].entries[str], dirs[m0] = mkdir(dirs[m0].size, md6, dirs[m0].nlink, dirs[m0].nsubdirs, entries0), files[entries0[str0]] = mkfile(m2, md, # links(entries0[str0], dirs), content1), files[entries[str]] = mkfile(m1, md3, files[entries[str]].nlink, content), dirs[m] = mkdir(dirs[m].size, md5, dirs[m].nlink, dirs[m].nsubdirs, entries), afs-cons(dirs, files), str0 ∈ dirs[m0].entries, str ∈ dirs[m].entries, entries0[str0] ∈ files, entries[str] ∈ files, m0 ∈ dirs, m ∈ dirs, str0 ∈ entries0, str ∈ entries, ¬ entries[str] ∈ dirs, m = m0 → md1 = md2, links(m0, dirs) ≠ ∅ ∨ m0 = ROOT_INO, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪fail#(; ; err); asynced := ?⟫ true

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 288:
# links(entries[str], dirs) = m4, # links(m0, dirs) = dirs[m0].nlink, # links(m, dirs) = dirs[m].nlink, dirs[m] = mkdir(dirs[m].size, md5, dirs[m].nlink, dirs[m].nsubdirs, entries), files[entries[str]] = mkfile(m1, md3, m4, content), files[entries0[str0]] = mkfile(m2, md, # links(entries0[str0], dirs), content1), dirs[m0] = mkdir(dirs[m0].size, md6, dirs[m0].nlink, dirs[m0].nsubdirs, entries0), entries[str] = dirs[m].entries[str], entries0[str0] = dirs[m0].entries[str0], files[entries[str]] = mkfile(m3, md0, m4, content0), afs-cons(dirs, files), str ∈ entries, str0 ∈ entries0, m ∈ dirs, m0 ∈ dirs, entries[str] ∈ files, entries0[str0] ∈ files, str ∈ dirs[m].entries, str0 ∈ dirs[m0].entries, m = m0 → md1 = md2, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO, links(m0, dirs) ≠ ∅ ∨ m0 = ROOT_INO ⊦ ⟪fail#(; ; err); asynced := ?⟫ true, entries[str] ∈ 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[entries[str]], m3, md0, m4, content0]

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[entries[str]], m3, md0, m4, content0