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Proof step 49 from proof inv-unlink (previous step)

# links(entries0[str], dirs0) = m1 + 1, (ino = m ⊃ mkdir(m2, md2, # links(m, dirs0), m3, entries0 -- str) ;mkdir(# entries, md3, # links(ino, dirs0), # subdirs(ino, dirs0), entries) ) = mkdir(m11, md4, m12, m13, entries1), (ino = entries0[str] ⊃ mkfile(m0, md1, m1, content);mkfile(m4, md, m5, content0)) = mkfile(m6, md0, m7, content1), dirs0[ino] = mkdir(# entries, md3, # links(ino, dirs0), # subdirs(ino, dirs0), entries), dirs0[m] = mkdir(m2 + 1, md2, # links(m, dirs0), m3, entries0), files0[entries0[str]] = mkfile(m0, md1, m1 + 1, content), files0[ino] = mkfile(m4, md, m5, content0), afs-cons(dirs0, files0), ROOT_INO ∈ dirs0, entries0[str] ∈ files0, str ∈ entries0, m ∈ dirs0, ino ∈ dirs0, # links(ino, dirs0) ≤ 1, name ∈ entries → entries[name] ∈ dirs0 ∨ entries[name] ∈ files0, ino ≠ ROOT_INO ∧ links(ino, dirs0) = ∅ → entries = ∅, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ ino = entries0[str], m12 = # (entries0[str] = ino ⊃ links(entries0[str], dirs0) -- mklink(m, str);links(ino, dirs0)) ∧ # (entries0[str] = ino ⊃ links(entries0[str], dirs0) -- mklink(m, str);links(ino, dirs0)) ≤ 1 ∧ m11 = # entries1 ∧ m13 = # subdirs(ino, dirs0[m, mkdir(m2, md2, # links(m, dirs0), m3, entries0 -- str)])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 50:
# links(entries0[str], dirs0) = m1 + 1, (ino = m ⊃ mkdir(m2, md2, # links(m, dirs0), m3, entries0 -- str) ;mkdir(# entries, md3, # links(ino, dirs0), # subdirs(ino, dirs0), entries) ) = mkdir(m11, md4, m12, m13, entries1), dirs0[ino] = mkdir(# entries, md3, # links(ino, dirs0), # subdirs(ino, dirs0), entries), dirs0[m] = mkdir(m2 + 1, md2, # links(m, dirs0), m3, entries0), files0[entries0[str]] = mkfile(m0, md1, m1 + 1, content), files0[ino] = mkfile(m4, md, m5, content0), afs-cons(dirs0, files0), ROOT_INO ∈ dirs0, entries0[str] ∈ files0, str ∈ entries0, m ∈ dirs0, ino ∈ dirs0, # links(ino, dirs0) ≤ 1, name ∈ entries → entries[name] ∈ dirs0 ∨ entries[name] ∈ files0, ino ≠ ROOT_INO ∧ links(ino, dirs0) = ∅ → entries = ∅, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ ino = entries0[str], m12 = # links(ino, dirs0) ∧ m11 = # entries1 ∧ m13 = # subdirs(ino, dirs0[m, mkdir(m2, md2, # links(m, dirs0), m3, entries0 -- str)])

Rule argument

Additional information

Used simplifier rules: ⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0; (ws)