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Proof step 194 from proof inv-link (previous step)

(m18 = m11 ⊃ mkdir(m1 + 1, md0, # links(m11, dirs0), m9, entries3[str0, entries2[str]]);mkdir(m14, md8, # links(m18, dirs0), m17, entries5)) = mkdir(m, md7, m3, m13, entries4), dirs0[ino1] = mkdir(m5, md2, # links(ino1, dirs0), m10, entries1), entries[str] = entries2[str], dirs0[ino0] = mkdir(m2, md1, # links(ino0, dirs0), m8, entries), entries0[str] = entries2[str], files0[entries2[str]] = mkfile(m0, md6, # links(entries2[str], dirs0), content0), dirs0[m11] = mkdir(m1, md5, # links(m11, dirs0), m9, entries3), dirs0[ino2] = mkdir(m4, md3, # links(ino2, dirs0), m6, entries0), entries1[str] = entries2[str], dirs0[ino3] = mkdir(m7, md4, # links(ino3, dirs0), m12, entries2), dirs0[m18] = mkdir(m14, md8, # links(m18, dirs0), m17, entries5), afs-cons(dirs0, files0), afs-cons (dirs0[m11, mkdir(m1 + 1, md0, # links(m11, dirs0), m9, entries3[str0, entries2[str]])], files0[entries2[str], mkfile(m15, md, # links(entries2[str], dirs0) + 1, content0)]), synced(dirs0, icache0, pcache), str ∈ entries1, ino1 ∈ dirs0, str ∈ entries, ino0 ∈ dirs0, ino2 ∈ dirs0, str ∈ entries0, ino3 ∈ dirs0, str ∈ entries2, m11 ∈ dirs0, entries2[str] ∈ files0, dentrykey(m18, str1) ∈ dcache[dentrykey(m11, str0), mkdentry(str0, entries2[str])], m18 ∈ dirs0, dentrykey(m18, str1) ∈ dcache → str1 = dcache[dentrykey(m18, str1)].name ∧ (links(m18, dirs0) ≠ ∅ ∨ m18 = ROOT_INO) ∧ (dcache[dentrykey(m18, str1)].ino ∈ dirs0 ∨ dcache[dentrykey(m18, str1)].ino ∈ files0) ∧ dcache[dentrykey(m18, str1)].name ∈ entries5 ∧ dcache[dentrykey(m18, str1)].ino = entries5[dcache[dentrykey(m18, str1)].name] ∧ dcache[dentrykey(m18, str1)].dentry?, asynced1 → synced(files0, icache0, pcache), ∀ key0. key0 ∈ dcache → key0.dentry? ∧ key0.name = dcache[key0].name ∧ key0.ino ∈ dirs0 ∧ (links(key0.ino, dirs0) ≠ ∅ ∨ key0.ino = ROOT_INO) ∧ (dcache[key0].ino ∈ dirs0 ∨ dcache[key0].ino ∈ files0) ∧ dcache[key0].name ∈ dirs0[key0.ino].entries ∧ dcache[key0].ino = dirs0[key0.ino].entries[dcache[key0].name] ∧ dcache[key0].dentry?, links(ino1, dirs0) ≠ ∅ ∨ ino1 = ROOT_INO, links(ino0, dirs0) ≠ ∅ ∨ ino0 = ROOT_INO, links(ino2, dirs0) ≠ ∅ ∨ ino2 = ROOT_INO, links(m11, dirs0) ≠ ∅ ∨ m11 = ROOT_INO, links(ino3, dirs0) ≠ ∅ ∨ ino3 = ROOT_INO ⊦ entries2[str] = m18, str0 ∈ entries3, str1 = dcache[dentrykey(m11, str0), mkdentry(str0, entries2[str])][dentrykey(m18, str1)].name ∧ (links(m18, dirs0) ≠ ∅ ∨ m18 = ROOT_INO) ∧ ( dcache[dentrykey(m11, str0), mkdentry(str0, entries2[str])][dentrykey(m18, str1)].ino ∈ dirs0 ∨ dcache[dentrykey(m11, str0), mkdentry(str0, entries2[str])][dentrykey(m18, str1)].ino ∈ files0) ∧ dcache[dentrykey(m11, str0), mkdentry(str0, entries2[str])][dentrykey(m18, str1)].name ∈ entries4 ∧ dcache[dentrykey(m11, str0), mkdentry(str0, entries2[str])][dentrykey(m18, str1)].ino = entries4[dcache[dentrykey(m11, str0), mkdentry(str0, entries2[str])][dentrykey(m18, str1)].name] ∧ dcache[dentrykey(m11, str0), mkdentry(str0, entries2[str])][dentrykey(m18, str1)].dentry?

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 195:
(m18 = m11 ⊃ mkdir(m1 + 1, md0, # links(m11, dirs0), m9, entries3[str0, entries2[str]]);mkdir(m14, md8, # links(m18, dirs0), m17, entries5)) = mkdir(m, md7, m3, m13, entries4), dirs0[m18] = mkdir(m14, md8, # links(m18, dirs0), m17, entries5), dirs0[ino3] = mkdir(m7, md4, # links(ino3, dirs0), m12, entries2), entries1[str] = entries2[str], dirs0[ino2] = mkdir(m4, md3, # links(ino2, dirs0), m6, entries0), dirs0[m11] = mkdir(m1, md5, # links(m11, dirs0), m9, entries3), files0[entries2[str]] = mkfile(m0, md6, # links(entries2[str], dirs0), content0), entries0[str] = entries2[str], dirs0[ino0] = mkdir(m2, md1, # links(ino0, dirs0), m8, entries), entries[str] = entries2[str], dirs0[ino1] = mkdir(m5, md2, # links(ino1, dirs0), m10, entries1), afs-cons (dirs0[m11, mkdir(m1 + 1, md0, # links(m11, dirs0), m9, entries3[str0, entries2[str]])], files0[entries2[str], mkfile(m15, md, # links(entries2[str], dirs0) + 1, content0)]), afs-cons(dirs0, files0), synced(dirs0, icache0, pcache), m18 ∈ dirs0, dentrykey(m18, str1) ∈ dcache[dentrykey(m11, str0), mkdentry(str0, entries2[str])], entries2[str] ∈ files0, m11 ∈ dirs0, str ∈ entries2, ino3 ∈ dirs0, str ∈ entries0, ino2 ∈ dirs0, ino0 ∈ dirs0, str ∈ entries, ino1 ∈ dirs0, str ∈ entries1, asynced1 → synced(files0, icache0, pcache), dentrykey(m18, str1) ∈ dcache → str1 = dcache[dentrykey(m18, str1)].name ∧ (links(m18, dirs0) ≠ ∅ ∨ m18 = ROOT_INO) ∧ (dcache[dentrykey(m18, str1)].ino ∈ dirs0 ∨ dcache[dentrykey(m18, str1)].ino ∈ files0) ∧ dcache[dentrykey(m18, str1)].name ∈ entries5 ∧ dcache[dentrykey(m18, str1)].ino = entries5[dcache[dentrykey(m18, str1)].name] ∧ dcache[dentrykey(m18, str1)].dentry?, ∀ key0. key0 ∈ dcache → key0.dentry? ∧ key0.name = dcache[key0].name ∧ key0.ino ∈ dirs0 ∧ (links(key0.ino, dirs0) ≠ ∅ ∨ key0.ino = ROOT_INO) ∧ (dcache[key0].ino ∈ dirs0 ∨ dcache[key0].ino ∈ files0) ∧ dcache[key0].name ∈ dirs0[key0.ino].entries ∧ dcache[key0].ino = dirs0[key0.ino].entries[dcache[key0].name] ∧ dcache[key0].dentry?, links(ino3, dirs0) ≠ ∅ ∨ ino3 = ROOT_INO, links(m11, dirs0) ≠ ∅ ∨ m11 = ROOT_INO, links(ino2, dirs0) ≠ ∅ ∨ ino2 = ROOT_INO, links(ino0, dirs0) ≠ ∅ ∨ ino0 = ROOT_INO, links(ino1, dirs0) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ entries2[str] = m18, dentrykey(m18, str1) = dentrykey(m11, str0), str0 ∈ entries3, str1 = dcache[dentrykey(m11, str0), mkdentry(str0, entries2[str])][dentrykey(m18, str1)].name ∧ (links(m18, dirs0) ≠ ∅ ∨ m18 = ROOT_INO) ∧ ( dcache[dentrykey(m11, str0), mkdentry(str0, entries2[str])][dentrykey(m18, str1)].ino ∈ dirs0 ∨ dcache[dentrykey(m11, str0), mkdentry(str0, entries2[str])][dentrykey(m18, str1)].ino ∈ files0) ∧ dcache[dentrykey(m11, str0), mkdentry(str0, entries2[str])][dentrykey(m18, str1)].name ∈ entries4 ∧ dcache[dentrykey(m11, str0), mkdentry(str0, entries2[str])][dentrykey(m18, str1)].ino = entries4[dcache[dentrykey(m11, str0), mkdentry(str0, entries2[str])][dentrykey(m18, str1)].name] ∧ dcache[dentrykey(m11, str0), mkdentry(str0, entries2[str])][dentrykey(m18, str1)].dentry?

Rule argument

fma: dentrykey(m18, str1) = dentrykey(m11, str0)

Additional information

Used simplifier rules: ⊦ dentrykey(m, str) = dentrykey(m0, str0) ↔ m = m0 ∧ str = str0; (ws)%⊦ mkdir(m, md, m0, m1, entries) = mkdir(m2, md0, m3, m4, entries0) ↔ m = m2 ∧ md = md0 ∧ m0 = m3 ∧ m1 = m4 ∧ entries = entries0; (ws)% ⊦ key ∈ dcache[key, dent]; (s)% ⊦ dcache[key, dent][key] = dent; (s)% ⊦ mkdentry(str, m).name = str; (s)% ⊦ mkdentry(str, m).ino = m; (s)% ⊦ str ∈ entries[str, ino]; (s)% ⊦ entries[str, ino][str] = ino; (s)% ⊦ mkdentry(str, m).dentry?; (s) Used formulas: dentrykey(m18, str1) = dentrykey(m11, str0)