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Proof step 112 from proof afs-cons-rename-file-negdentry (previous step)

(m0 = m ⊃ mkdir(m1 + 1, md0, m4, m6, entries0[str0, entries1[str]]);mkdir(m1 + 1, md4, m4, m6, entries0[str0, entries1[str]])).meta:= md1 = mkdir(m14, md7, m15, m16, entries3), (m0 = m ⊃ mkdir(m2, md2, # links(m, dirs0), m5, entries1 -- str) ;mkdir(# entries, md6, # links(m0, dirs0), # subdirs(m0, dirs0), entries) ) = mkdir(m1, md4, m4, m6, entries0), files[m0] = mkfile(m8, md3, m10, content), dirs0[m0] = mkdir(# entries, md6, # links(m0, dirs0), # subdirs(m0, dirs0), entries), files[entries1[str]] = mkfile(m3, md, # links(entries1[str], dirs0), content0), dirs0[m] = mkdir(m2 + 1, md2, # links(m, dirs0), m5, entries1), afs-cons(dirs0, files), m ∈ dirs0, entries1[str] ∈ files, str ∈ entries1, ROOT_INO ∈ dirs0, m0 ∈ dirs0, # links(m0, dirs0) ≤ 1, m0 ≠ ROOT_INO ∧ links(m0, dirs0) = ∅ → entries = ∅, name ∈ entries → entries[name] ∈ dirs0 ∨ entries[name] ∈ files, m0 = m → md1 = md0, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ m14 = # entries3, str0 ∈ entries, entries1[str] ∈ dirs0

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 113:
(m0 = m ⊃ mkdir(m1 + 1, md0, m4, m6, entries0[str0, entries1[str]]);mkdir(m1 + 1, md4, m4, m6, entries0[str0, entries1[str]])).meta:= md1 = mkdir(m14, md7, m15, m16, entries3), (m0 = m ⊃ mkdir(m2, md2, # links(m, dirs0), m5, entries1 -- str) ;mkdir(# entries, md6, # links(m0, dirs0), # subdirs(m0, dirs0), entries) ) = mkdir(m1, md4, m4, m6, entries0), dirs0[m] = mkdir(m2 + 1, md2, # links(m, dirs0), m5, entries1), files[entries1[str]] = mkfile(m3, md, # links(entries1[str], dirs0), content0), dirs0[m0] = mkdir(# entries, md6, # links(m0, dirs0), # subdirs(m0, dirs0), entries), files[m0] = mkfile(m8, md3, m10, content), m0 = m, afs-cons(dirs0, files), m0 ∈ dirs0, ROOT_INO ∈ dirs0, str ∈ entries1, entries1[str] ∈ files, m ∈ dirs0, # links(m0, dirs0) ≤ 1, m0 = m → md1 = md0, name ∈ entries → entries[name] ∈ dirs0 ∨ entries[name] ∈ files, m0 ≠ ROOT_INO ∧ links(m0, dirs0) = ∅ → entries = ∅, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ m14 = # entries3, entries1[str] ∈ dirs0, str0 ∈ entries

Rule argument

fma: m0 = m

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 + 1; (s)% ⊦ m + n = m + n0 ↔ n = n0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic Used formulas: m0 = m