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Proof step 172 from proof inv-unlink (previous step)

# links(entries0[str], dirs0) = m2 + 1, dcache[key].ino = dirs0[m6].entries[str0], (m6 = m0 ⊃ mkdir(m8, md3, # links(m6, dirs0), m7, entries0 -- str);dirs0[m6]) = mkdir(m, md, m4, m5, entries), files0[entries0[str]] = mkfile(m1, md1, m2 + 1, content0), dirs0[m0] = mkdir(m8 + 1, md2, # links(m0, dirs0), m7, entries0), key = dentrykey(m6, str0), str0 = dcache[key].name, dcache[key].dentry?, key.dentry?, afs-cons(dirs0[m0, mkdir(m8, md3, # links(m0, dirs0), m7, entries0 -- str)], files0[entries0[str], mkfile(m3, md0, m2, content0)]), afs-cons(dirs0, files0), synced(dirs0, icache0, pcache), str0 ∈ dirs0[m6].entries, m6 ∈ dirs0, m0 ∈ dirs0, entries0[str] ∈ files0, str ∈ entries0, key ∈ dcache, 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?, dcache[key].ino ∈ dirs0 ∨ dcache[key].ino ∈ files0, links(m6, dirs0) ≠ ∅ ∨ m6 = ROOT_INO, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ key = dentrykey(m0, str), ((entries0[str] = m6 ⊃ links(m6, dirs0) -- mklink(m0, str);links(m6, dirs0)) ≠ ∅ ∨ m6 = ROOT_INO) ∧ str0 ∈ entries ∧ dcache[key].ino = entries[str0]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 173:
# links(entries0[str], dirs0) = m2 + 1, dcache[key].ino = dirs0[m6].entries[dcache[key].name], (m6 = m0 ⊃ mkdir(m8, md3, # links(m0, dirs0), m7, entries0 -- str);dirs0[m6]) = mkdir(m, md, m4, m5, entries), dirs0[m0] = mkdir(m8 + 1, md2, # links(m0, dirs0), m7, entries0), files0[entries0[str]] = mkfile(m1, md1, m2 + 1, content0), key = dentrykey(m6, dcache[key].name), key.dentry?, dcache[key].dentry?, afs-cons(dirs0, files0), afs-cons(dirs0[m0, mkdir(m8, md3, # links(m0, dirs0), m7, entries0 -- str)], files0[entries0[str], mkfile(m3, md0, m2, content0)]), synced(dirs0, icache0, pcache), key ∈ dcache, str ∈ entries0, entries0[str] ∈ files0, m0 ∈ dirs0, m6 ∈ dirs0, dcache[key].name ∈ dirs0[m6].entries, 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(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO, links(m6, dirs0) ≠ ∅ ∨ m6 = ROOT_INO, dcache[key].ino ∈ dirs0 ∨ dcache[key].ino ∈ files0 ⊦ key = dentrykey(m0, str), ((entries0[str] = m6 ⊃ links(entries0[str], dirs0) -- mklink(m0, str);links(m6, dirs0)) ≠ ∅ ∨ m6 = ROOT_INO) ∧ dcache[key].name ∈ entries ∧ dcache[key].ino = entries[dcache[key].name]

Proof step 172 from proof inv-unlink (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

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