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Proof step 155 from proof afs-cons-rename-file-dentry (previous step)

# links(entries[str], dirs0) = m11 + 1, (entries1[str0] = entries[str] ⊃ mkfile(m2, md, m11, content1);mkfile(m1, md3, # links(entries1[str0], dirs0), content)) = mkfile(m14, md8, m15, content2), files0[entries[str]] = mkfile(m5, md0, m11 + 1, content1), dirs0[m] = mkdir(m6, md6, # links(m, dirs0), m10, entries), files0[entries1[str0]] = mkfile(m1, md3, # links(entries1[str0], dirs0), content), dirs0[entries1[str0]] = mkdir(m16, md9, m17, m18, entries2), dirs0[m0] = mkdir(m3 + 1, md4, # links(m0, dirs0), m7, entries1), afs-cons(dirs0, files0), ROOT_INO ∈ dirs0, entries[str] ∈ files0, m0 ∈ dirs0, str ∈ entries, str0 ∈ entries1, entries1[str0] ∈ files0, m ∈ dirs0, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ m0 = m, m15 = #((links(entries1[str0], dirs0) -- mklink(m0, str0)) ++ mklink(m, str)), entries[str] ∈ dirs0, entries1[str0] ∈ dirs0

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 156:
# links(entries[str], dirs0) = m11 + 1, (entries1[str0] = entries[str] ⊃ mkfile(m2, md, m11, content1);mkfile(m1, md3, # links(entries1[str0], dirs0), content)) = mkfile(m14, md8, m15, content2), dirs0[m0] = mkdir(m3 + 1, md4, # links(m0, dirs0), m7, entries1), dirs0[entries1[str0]] = mkdir(m16, md9, m17, m18, entries2), files0[entries1[str0]] = mkfile(m1, md3, # links(entries1[str0], dirs0), content), dirs0[m] = mkdir(m6, md6, # links(m, dirs0), m10, entries), files0[entries[str]] = mkfile(m5, md0, m11 + 1, content1), afs-cons(dirs0, files0), m ∈ dirs0, entries1[str0] ∈ files0, str0 ∈ entries1, str ∈ entries, m0 ∈ dirs0, entries[str] ∈ files0, ROOT_INO ∈ dirs0, mklink(m, str) ∈ links(entries1[str0], dirs0) -- mklink(m0, str0), links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ m0 = m, m15 = #((links(entries1[str0], dirs0) -- mklink(m0, str0)) ++ mklink(m, str)), entries1[str0] ∈ dirs0, entries[str] ∈ dirs0
Proof step 158:
# links(entries[str], dirs0) = m11 + 1, (entries1[str0] = entries[str] ⊃ mkfile(m2, md, m11, content1);mkfile(m1, md3, # links(entries1[str0], dirs0), content)) = mkfile(m14, md8, m15, content2), dirs0[m0] = mkdir(m3 + 1, md4, # links(m0, dirs0), m7, entries1), dirs0[entries1[str0]] = mkdir(m16, md9, m17, m18, entries2), files0[entries1[str0]] = mkfile(m1, md3, # links(entries1[str0], dirs0), content), dirs0[m] = mkdir(m6, md6, # links(m, dirs0), m10, entries), files0[entries[str]] = mkfile(m5, md0, m11 + 1, content1), afs-cons(dirs0, files0), m ∈ dirs0, entries1[str0] ∈ files0, str0 ∈ entries1, str ∈ entries, m0 ∈ dirs0, entries[str] ∈ files0, ROOT_INO ∈ dirs0, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ m0 = m, m15 = #((links(entries1[str0], dirs0) -- mklink(m0, str0)) ++ mklink(m, str)), entries1[str0] ∈ dirs0, entries[str] ∈ dirs0, mklink(m, str) ∈ links(entries1[str0], dirs0) -- mklink(m0, str0)

Rule argument

fma: mklink(m, str) ∈ links(entries1[str0], dirs0) -- mklink(m0, str0)

Additional information

Used formulas: mklink(m, str) ∈ links(entries1[str0], dirs0) -- mklink(m0, str0)