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Proof step 504 from proof inv-rename-file-dentry (previous step)

(m8 = m3 ⊃ mkdir(m1, md2, # links(m3, dirs0), m4, entries);mkdir(m7, md4, # links(m8, dirs0), m9, entries1)) = mkdir(m2, md, m5, m6, entries0), dirs0[m8] = mkdir(m7, md4, # links(m8, dirs0), m9, entries1), files[entries[str0]] = mkfile(m0, md0, # links(entries[str0], dirs0), content), dirs0[m3] = mkdir(m1, md1, # links(m3, dirs0), m4, entries), dcache0[key] = mkdentry(str, m10), key = dentrykey(m8, str), m10 = entries1[str], key.dentry?, dcache0[key].dentry?, afs-cons (dirs0[m3, mkdir(m1, md2, # links(m3, dirs0), m4, entries)], files[entries[str0], mkfile(m, md3, # links(entries[str0], dirs0), content)]), afs-cons(dirs0, files), synced(dirs0, icache0, pcache), entries[str0] ∈ files, str0 ∈ entries, m3 ∈ dirs0, key ∈ dcache0, m8 ∈ dirs0, str ∈ entries1, asynced2 → synced(files, icache0, pcache), ∀ key0. key0 ∈ dcache0 → key0.dentry? ∧ key0.name = dcache0[key0].name ∧ key0.ino ∈ dirs0 ∧ (links(key0.ino, dirs0) ≠ ∅ ∨ key0.ino = ROOT_INO) ∧ (dcache0[key0].ino ∈ dirs0 ∨ dcache0[key0].ino ∈ files) ∧ dcache0[key0].name ∈ dirs0[key0.ino].entries ∧ dcache0[key0].ino = dirs0[key0.ino].entries[dcache0[key0].name] ∧ dcache0[key0].dentry?, links(m3, dirs0) ≠ ∅ ∨ m3 = ROOT_INO, links(m8, dirs0) ≠ ∅ ∨ m8 = ROOT_INO, m10 ∈ dirs0 ∨ m10 ∈ files ⊦ key = dentrykey(m3, str0), entries[str0] ∈ dirs0, str ∈ entries0 ∧ m10 = entries0[str]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 505:
(m8 = m3 ⊃ mkdir(m1, md2, # links(m3, dirs0), m4, entries);mkdir(m7, md4, # links(m8, dirs0), m9, entries1)) = mkdir(m2, md, m5, m6, entries0), dirs0[m8] = mkdir(m7, md4, # links(m8, dirs0), m9, entries1), files[entries[str0]] = mkfile(m0, md0, # links(entries[str0], dirs0), content), dirs0[m3] = mkdir(m1, md1, # links(m3, dirs0), m4, entries), dcache0[dentrykey(m8, str)] = mkdentry(str, entries1[str]), afs-cons (dirs0[m3, mkdir(m1, md2, # links(m3, dirs0), m4, entries)], files[entries[str0], mkfile(m, md3, # links(entries[str0], dirs0), content)]), afs-cons(dirs0, files), synced(dirs0, icache0, pcache), entries[str0] ∈ files, str0 ∈ entries, m3 ∈ dirs0, dentrykey(m8, str) ∈ dcache0, m8 ∈ dirs0, str ∈ entries1, asynced2 → synced(files, icache0, pcache), ∀ key0. key0 ∈ dcache0 → key0.dentry? ∧ key0.name = dcache0[key0].name ∧ key0.ino ∈ dirs0 ∧ (links(key0.ino, dirs0) ≠ ∅ ∨ key0.ino = ROOT_INO) ∧ (dcache0[key0].ino ∈ dirs0 ∨ dcache0[key0].ino ∈ files) ∧ dcache0[key0].name ∈ dirs0[key0.ino].entries ∧ dcache0[key0].ino = dirs0[key0.ino].entries[dcache0[key0].name] ∧ dcache0[key0].dentry?, links(m3, dirs0) ≠ ∅ ∨ m3 = ROOT_INO, links(m8, dirs0) ≠ ∅ ∨ m8 = ROOT_INO, entries1[str] ∈ dirs0 ∨ entries1[str] ∈ files ⊦ dentrykey(m8, str) = dentrykey(m3, str0), entries[str0] ∈ dirs0, str ∈ entries0 ∧ entries1[str] = entries0[str]

Rule argument

Additional information

Used simplifier rules: ⊦ mkdentry(str, m).dentry?; (s)% ⊦ dentrykey(m, str).dentry?; (s)