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Proof step 177 from proof afs-cons-rename-dir-negdentry (previous step)

(ino = m ⊃ mkdir(m4 + 1, md1, # links(m, dirs0), m7 + 1, (entries3 -- str)[str0, entries3[str]]) ;mkdir(# entries, md6, # links(ino, dirs0), # subdirs(ino, dirs0), entries) ) = mkdir(m15, md7, m16, m17, entries4), dirs0[entries3[str]] = mkdir(m3, md4, # links(entries3[str], dirs0), m5, entries1), dirs0[ino] = mkdir(# entries, md6, # links(ino, dirs0), # subdirs(ino, dirs0), entries), files[ino] = mkfile(m9, md2, m11, content), dirs0[m] = mkdir(m4 + 1, md5, # links(m, dirs0), m7 + 1, entries3), ino = m, afs-cons(dirs0, files), m ∈ dirs0, str ∈ entries3, entries3[str] ∈ dirs0, ROOT_INO ∈ dirs0, name ∈ entries4, ino ∈ dirs0, # links(ino, dirs0) ≤ 1, ino ≠ ROOT_INO ∧ links(ino, dirs0) = ∅ → entries = ∅, name ∈ entries → entries[name] ∈ dirs0 ∨ entries[name] ∈ files, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ entries4[name] ∈ files, entries4[name] ∈ dirs0, str0 ∈ entries3

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 178:
# subdirs(m, dirs0) = m7 + 1, # entries3 = m4 + 1, files[m] = mkfile(m9, md2, m11, content), dirs0[m] = mkdir(m4 + 1, md5, # links(m, dirs0), m7 + 1, entries3), dirs0[entries3[str]] = mkdir(m3, md4, # links(entries3[str], dirs0), m5, entries1), afs-cons(dirs0, files), name ∈ (entries3 -- str)[str0, entries3[str]], ROOT_INO ∈ dirs0, entries3[str] ∈ dirs0, str ∈ entries3, m ∈ dirs0, # links(m, dirs0) ≤ 1, name ∈ entries3 → entries3[name] ∈ dirs0 ∨ entries3[name] ∈ files, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ entries3 = ∅, str0 ∈ entries3, (entries3 -- str)[str0, entries3[str]][name] ∈ dirs0, (entries3 -- str)[str0, entries3[str]][name] ∈ files, m ≠ ROOT_INO ∧ links(m, dirs0) = ∅

Rule argument

Additional information

Used simplifier rules: c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + n = 0 ↔ m = 0 ∧ n = 0; (ws)% ⊦ # ∅ = 0; (s)%⊦ mkdir(m, md, m0, m1, entries) = mkdir(m2, md0, m3, m4, entries0) ↔ m = m2 ∧ md = md0 ∧ m0 = m3 ∧ m1 = m4 ∧ entries = entries0; (ws)