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Proof step 163 from proof afs-cons-rename-file-negdentry (previous step)

# links(entries0[str], dirs0) = files[entries0[str]].nlink, # links(m0, dirs0) = dirs0[m0].nlink, # links(m, dirs0) = dirs0[m].nlink, dirs0[m].size = 0, entries0[str] = dirs0[m].entries[str], dirs0[m0] = mkdir(dirs0[m0].size, md3, dirs0[m0].nlink, dirs0[m0].nsubdirs, entries), files[entries0[str]] = mkfile(m1, md2, files[entries0[str]].nlink, content), dirs0[m] = mkdir(0, md4, dirs0[m].nlink, dirs0[m].nsubdirs, entries0), afs-cons(dirs0, files), str ∈ dirs0[m].entries, m0 ∈ dirs0, entries0[str] ∈ files, m ∈ dirs0, str ∈ entries0, m0 = m → md1 = md0, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ str0 ∈ dirs0[m0].entries, str0 ∈ entries

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 164:
# links(m, dirs0) = dirs0[m].nlink, # links(m0, dirs0) = dirs0[m0].nlink, # links(entries0[str], dirs0) = m3, dirs0[m].size = 0, dirs0[m] = mkdir(0, md4, dirs0[m].nlink, dirs0[m].nsubdirs, entries0), files[entries0[str]] = mkfile(m1, md2, m3, content), dirs0[m0] = mkdir(dirs0[m0].size, md3, dirs0[m0].nlink, dirs0[m0].nsubdirs, entries), entries0[str] = dirs0[m].entries[str], files[entries0[str]] = mkfile(m2, md, m3, content0), afs-cons(dirs0, files), str ∈ entries0, m ∈ dirs0, entries0[str] ∈ files, m0 ∈ dirs0, str ∈ dirs0[m].entries, m0 = m → md1 = md0, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ str0 ∈ entries, str0 ∈ dirs0[m0].entries

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[entries0[str]], m2, md, m3, 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[entries0[str]], m2, md, m3, content0