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Proof step 400 from proof inv-rename-file-dentry (previous step)

files[entries[str0]] = mkfile(m0, md0, # links(entries[str0], dirs0), content), dirs0[m3] = mkdir(m1, md1, # links(m3, dirs0), m4, entries), err = ESUCCESS, icache = icache0[m3, mkientry(false, mkinode(m3, md2, true, # links(m3, dirs0), m4, m1))], afs-cons (dirs0[m3, mkdir(m1, md2, # links(m3, dirs0), m4, entries)], files[entries[str0], mkfile(m2, md, # links(entries[str0], dirs0), content)]), afs-cons(dirs0, files), dcache-cons(dcache, dirs0, files), icache-cons(icache0, dirs0, files), pcache-cons(pcache, dirs0, files), synced(dirs0, icache0, pcache), entries[str0] ∈ files, str0 ∈ entries, m3 ∈ dirs0, ¬ entries[str0] ∈ dirs0, asynced2 → synced(files, icache0, pcache), links(m3, dirs0) ≠ ∅ ∨ m3 = ROOT_INO ⊦ ⟪icache_set# (mkinode (entries[str0], files[entries[str0], mkfile(m2, md, # links(entries[str0], dirs0), content)][entries[str0]].meta, false, files[entries[str0], mkfile(m2, md, # links(entries[str0], dirs0), content)][entries[str0]].nlink, 0, files[entries[str0], mkfile(m2, md, # links(entries[str0], dirs0), content)][entries[str0]].size), false ; err, icache); dcache_delete#(m3, mkdentry(str0, entries[str0]).name; err, dcache); dcache_set# (m3, mkdentry(mkdentry(str0, entries[str0]).name, mkdentry(str0, entries[str0]).ino).name, mkdentry(mkdentry(str0, entries[str0]).name, mkdentry(str0, entries[str0]).ino) ; err, dcache)⟫ ( icache-cons (icache, dirs0[m3, mkdir(m1, md2, # links(m3, dirs0), m4, entries)], files[entries[str0], (files[entries[str0]].size:= m2).meta:= md]) ∧ dcache-cons (dcache, dirs0[m3, mkdir(m1, md2, # links(m3, dirs0), m4, entries)], files[entries[str0], (files[entries[str0]].size:= m2).meta:= md]) ∧ pcache-cons (pcache, dirs0[m3, mkdir(m1, md2, # links(m3, dirs0), m4, entries)], files[entries[str0], (files[entries[str0]].size:= m2).meta:= md]) ∧ synced(dirs0[m3, mkdir(m1, md2, # links(m3, dirs0), m4, entries)], icache, pcache) ∧ (asynced2 → synced(files[entries[str0], (files[entries[str0]].size:= m2).meta:= md], icache, pcache)))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 401:
dirs0[m3] = mkdir(m1, md1, # links(m3, dirs0), m4, entries), files[entries[str0]] = mkfile(m0, md0, # links(entries[str0], dirs0), content), files[entries[str0], mkfile(m2, md, # links(entries[str0], dirs0), content)][entries[str0]] = mkfile(m, md3, m5, content0), err = ESUCCESS, icache = icache0[m3, mkientry(false, mkinode(m3, md2, true, # links(m3, dirs0), m4, m1))], afs-cons(dirs0, files), afs-cons (dirs0[m3, mkdir(m1, md2, # links(m3, dirs0), m4, entries)], files[entries[str0], mkfile(m2, md, # links(entries[str0], dirs0), content)]), dcache-cons(dcache, dirs0, files), icache-cons(icache0, dirs0, files), pcache-cons(pcache, dirs0, files), synced(dirs0, icache0, pcache), m3 ∈ dirs0, str0 ∈ entries, entries[str0] ∈ files, asynced2 → synced(files, icache0, pcache), links(m3, dirs0) ≠ ∅ ∨ m3 = ROOT_INO ⊦ ⟪icache_set#(mkinode(entries[str0], md3, false, m5, 0, m), false; err, icache); dcache_delete#(m3, mkdentry(str0, entries[str0]).name; err, dcache); dcache_set# (m3, mkdentry(mkdentry(str0, entries[str0]).name, mkdentry(str0, entries[str0]).ino).name, mkdentry(mkdentry(str0, entries[str0]).name, mkdentry(str0, entries[str0]).ino) ; err, dcache)⟫ ( icache-cons (icache, dirs0[m3, mkdir(m1, md2, # links(m3, dirs0), m4, entries)], files[entries[str0], (files[entries[str0]].size:= m2).meta:= md]) ∧ dcache-cons (dcache, dirs0[m3, mkdir(m1, md2, # links(m3, dirs0), m4, entries)], files[entries[str0], (files[entries[str0]].size:= m2).meta:= md]) ∧ pcache-cons (pcache, dirs0[m3, mkdir(m1, md2, # links(m3, dirs0), m4, entries)], files[entries[str0], (files[entries[str0]].size:= m2).meta:= md]) ∧ synced(dirs0[m3, mkdir(m1, md2, # links(m3, dirs0), m4, entries)], icache, pcache) ∧ (asynced2 → synced(files[entries[str0], (files[entries[str0]].size:= m2).meta:= md], icache, pcache))), entries[str0] ∈ dirs0

Rule argument

spec: abstract-file name: elim seq: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content) subst: [af, m, md, m0, content] → [files [entries[str0], mkfile(m2, md, # links(entries[str0], dirs0), content) ] [entries[str0] ], m, md3, m5, content0]

Additional information

Used simplifier rules: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content); (elim) Used terms: files [entries[str0], mkfile(m2, md, # links(entries[str0], dirs0), content) ] [entries[str0] ], m, md3, m5, content0