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Proof step 149 from proof inv-create (previous step)

(key.ino = m1 ⊃ mkdir(m0 + 1, md1, # links(key.ino, dirs0), m4, entries1[str, ino0]);mkdir(m5, md3, m6, m7, entries0)) = mkdir(m, md0, m2, m3, entries), dirs0[m1] = mkdir(m0, md2, # links(m1, dirs0), m4, entries1), dirs0[key.ino] = mkdir(m5, md3, m6, m7, entries0), afs-cons(dirs0[m1, mkdir(m0 + 1, md1, # links(m1, dirs0), m4, entries1[str, ino0])], (files0 ++ ino0)[ino0, mkfile(0, md, 1, ∅)]), afs-cons(dirs0, files0), synced(dirs0, icache0, pcache), m1 ∈ dirs0, key ∈ dcache[dentrykey(m1, str), mkdentry(str, ino0)], key ∈ dcache → key.dentry? ∧ key.name = dcache[key].name ∧ key.ino ∈ dirs0 ∧ (links(key.ino, dirs0) ≠ ∅ ∨ key.ino = ROOT_INO) ∧ (dcache[key].ino ∈ dirs0 ∨ dcache[key].ino ∈ files0) ∧ dcache[key].name ∈ entries0 ∧ dcache[key].ino = entries0[dcache[key].name] ∧ dcache[key].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(m1, dirs0) ≠ ∅ ∨ m1 = ROOT_INO ⊦ ino0 = 0, key = dentrykey(m1, str), str ∈ entries1, ino0 ∈ files0, ino0 ∈ dirs0, key.dentry? ∧ key.name = dcache[dentrykey(m1, str), mkdentry(str, ino0)][key].name ∧ key.ino ∈ dirs0 ∧ (links(key.ino, dirs0) ≠ ∅ ∨ key.ino = ROOT_INO) ∧ ( dcache[dentrykey(m1, str), mkdentry(str, ino0)][key].ino ∈ dirs0 ∨ dcache[dentrykey(m1, str), mkdentry(str, ino0)][key].ino = ino0 ∨ dcache[dentrykey(m1, str), mkdentry(str, ino0)][key].ino ∈ files0) ∧ dcache[dentrykey(m1, str), mkdentry(str, ino0)][key].name ∈ entries ∧ dcache[dentrykey(m1, str), mkdentry(str, ino0)][key].ino = entries[dcache[dentrykey(m1, str), mkdentry(str, ino0)][key].name] ∧ dcache[dentrykey(m1, str), mkdentry(str, ino0)][key].dentry?

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 150:
dcache[key].ino = entries0[key.name], key.name = dcache[key].name, (key.ino = m1 ⊃ mkdir(m0 + 1, md1, # links(key.ino, dirs0), m4, entries1[str, ino0]);mkdir(m5, md3, # links(key.ino, dirs0), m7, entries0)) = mkdir(m, md0, m2, m3, entries), dirs0[m1] = mkdir(m0, md2, # links(m1, dirs0), m4, entries1), dirs0[key.ino] = mkdir(m5, md3, # links(key.ino, dirs0), m7, entries0), dcache[key].dentry?, key.dentry?, afs-cons(dirs0[m1, mkdir(m0 + 1, md1, # links(m1, dirs0), m4, entries1[str, ino0])], (files0 ++ ino0)[ino0, mkfile(0, md, 1, ∅)]), afs-cons(dirs0, files0), synced(dirs0, icache0, pcache), key.name ∈ entries0, key.ino ∈ dirs0, key ∈ dcache, m1 ∈ dirs0, 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?, entries0[key.name] ∈ dirs0 ∨ entries0[key.name] ∈ files0, links(key.ino, dirs0) ≠ ∅ ∨ key.ino = ROOT_INO, links(m1, dirs0) ≠ ∅ ∨ m1 = ROOT_INO ⊦ ino0 = 0, key = dentrykey(m1, str), str ∈ entries1, ino0 ∈ files0, ino0 ∈ dirs0, (entries0[key.name] ∈ dirs0 ∨ entries0[key.name] = ino0 ∨ entries0[key.name] ∈ files0) ∧ key.name ∈ entries ∧ entries0[key.name] = entries[key.name]

Rule argument

Additional information

Used simplifier rules: afs-cons-dir-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs ∧ dirs[ino] = mkdir(n0, md, n, n1, entries) → # links(ino, dirs) = n; (forward) from specification afs-base% ⊦ key ≠ key0 → dcache[key0, dent][key] = dcache[key]; (s)% ⊦ key ≠ key0 → (key ∈ dcache[key0, dent] ↔ key ∈ dcache); (s)