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Proof step 128 from proof afs-cons-rename-file-dentry (previous step)

# links(entries2[str], dirs0) = m11 + 1, (m = m0 ⊃ mkdir(m6, md2, m9, m10, entries[str, entries1[str0]]);mkdir(m6, md5, m9, m10, entries[str, entries1[str0]])).meta:= md1 = mkdir(m19, md10, m20, m21, entries3), (m = m0 ⊃ mkdir(m3, md4, # links(m0, dirs0), m7, entries1 -- str0) ;mkdir(# entries2, md9, # links(m, dirs0), # subdirs(m, dirs0), entries2) ) = mkdir(m6, md5, m9, m10, entries), dirs0[m0] = mkdir(m3 + 1, md4, # links(m0, dirs0), m7, entries1), files0[entries1[str0]] = mkfile(m1, md3, # links(entries1[str0], dirs0), content), files0[entries2[str]] = mkfile(m5, md0, m11 + 1, content1), dirs0[m] = mkdir(# entries2, md9, # links(m, dirs0), # subdirs(m, dirs0), entries2), files0[m] = mkfile(m12, md7, m13, content0), afs-cons(dirs0, files0), ROOT_INO ∈ dirs0, entries2[str] ∈ files0, m0 ∈ dirs0, str ∈ entries2, entries1[str0] ∈ files0, str0 ∈ entries1, m ∈ dirs0, # links(m, dirs0) ≤ 1, m = m0 → md1 = md2, name ∈ entries2 → entries2[name] ∈ dirs0 ∨ entries2[name] ∈ files0, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ entries2 = ∅, m19 = # entries3, entries2[str] ∈ dirs0, entries1[str0] ∈ dirs0, m0 = m ∧ mkdentry(str, entries2[str]) = mkdentry(str0, entries1[str0]), m ≠ ROOT_INO ∧ links(m, dirs0) = ∅

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 129:
# links(entries2[str], dirs0) = m11 + 1, (m = m0 ⊃ mkdir(m6, md2, m9, m10, entries[str, entries1[str0]]);mkdir(m6, md5, m9, m10, entries[str, entries1[str0]])).meta:= md1 = mkdir(m19, md10, m20, m21, entries3), (m = m0 ⊃ mkdir(m3, md4, # links(m0, dirs0), m7, entries1 -- str0) ;mkdir(# entries2, md9, # links(m, dirs0), # subdirs(m, dirs0), entries2) ) = mkdir(m6, md5, m9, m10, entries), files0[m] = mkfile(m12, md7, m13, content0), dirs0[m] = mkdir(# entries2, md9, # links(m, dirs0), # subdirs(m, dirs0), entries2), files0[entries2[str]] = mkfile(m5, md0, m11 + 1, content1), files0[entries1[str0]] = mkfile(m1, md3, # links(entries1[str0], dirs0), content), dirs0[m0] = mkdir(m3 + 1, md4, # links(m0, dirs0), m7, entries1), m = m0, afs-cons(dirs0, files0), m ∈ dirs0, str0 ∈ entries1, entries1[str0] ∈ files0, str ∈ entries2, m0 ∈ dirs0, entries2[str] ∈ files0, ROOT_INO ∈ dirs0, # links(m, dirs0) ≤ 1, name ∈ entries2 → entries2[name] ∈ dirs0 ∨ entries2[name] ∈ files0, m = m0 → md1 = md2, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ entries2 = ∅, m19 = # entries3, entries1[str0] ∈ dirs0, entries2[str] ∈ dirs0, m ≠ ROOT_INO ∧ links(m, dirs0) = ∅, m0 = m ∧ mkdentry(str, entries2[str]) = mkdentry(str0, entries1[str0])

Rule argument

fma: m = m0

Additional information

Used simplifier rules: ⊦ mkdir(m, md, m0, m1, entries) = mkdir(m2, md0, m3, m4, entries0) ↔ m = m2 ∧ md = md0 ∧ m0 = m3 ∧ m1 = m4 ∧ entries = entries0; (ws)%⊦ mkdir(m, md, m0, m1, entries).meta:= md0 = mkdir(m, md0, m0, m1, entries); (s)% ⊦ str ∈ entries → # entries[str, ino] = # entries; (s) Used formulas: m = m0