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Proof step 473 from proof inv-rename-file-dentry (previous step)

dirs0[m3] = mkdir(m1, md1, # links(m3, dirs0), m4, entries), files[entries[str0]] = mkfile(m0, md0, # links(entries[str0], dirs0), content), afs-cons(dirs0, files), afs-cons (dirs0[m3, mkdir(m1, md2, # links(m3, dirs0), m4, entries)], files[entries[str0], mkfile(m, md3, # links(entries[str0], dirs0), content)]), pcache-cons(pcache, dirs0, files), synced(dirs0, icache0, pcache), key ∈ pcache, m3 ∈ dirs0, str0 ∈ entries, entries[str0] ∈ files, asynced2 → synced(files, icache0, pcache), links(m3, dirs0) ≠ ∅ ∨ m3 = ROOT_INO ⊦ entries[str0] ∈ dirs0, key.data? ∧ # pcache[key].page = VFS_PAGE_SIZE ∧ key.ino ∈ files ∧ ( ¬ pcache[key].dirty → key.part ∈ (key.ino = entries[str0] ⊃ mkfile(m, md3, # links(entries[str0], dirs0), content);files[key.ino]).content ∧ pcache[key].page = (key.ino = entries[str0] ⊃ mkfile(m, md3, # links(entries[str0], dirs0), content);files[key.ino]).content[key.part])

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 474:
files[entries[str0]] = mkfile(m0, md0, # links(entries[str0], dirs0), content), dirs0[m3] = mkdir(m1, md1, # links(m3, dirs0), m4, entries), pcache[key] = mkpentry(boolvar, buf), 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), pcache-cons(pcache, dirs0, files), synced(dirs0, icache0, pcache), entries[str0] ∈ files, str0 ∈ entries, m3 ∈ dirs0, key ∈ pcache, asynced2 → synced(files, icache0, pcache), links(m3, dirs0) ≠ ∅ ∨ m3 = ROOT_INO ⊦ entries[str0] ∈ dirs0, key.data? ∧ # buf = VFS_PAGE_SIZE ∧ key.ino ∈ files ∧ ( ¬ boolvar → key.part ∈ (key.ino = entries[str0] ⊃ mkfile(m, md3, # links(entries[str0], dirs0), content);files[key.ino]).content ∧ buf = (key.ino = entries[str0] ⊃ mkfile(m, md3, # links(entries[str0], dirs0), content);files[key.ino]).content[key.part])

Rule argument

spec: pcache-entry name: elim seq: ⊦ (boolvar ↔ pe.dirty) ∧ buf = pe.page ↔ pe = mkpentry(boolvar, buf) subst: [pe, boolvar, buf] → [pcache[key], boolvar, buf]

Additional information

Used simplifier rules: ⊦ (boolvar ↔ pe.dirty) ∧ buf = pe.page ↔ pe = mkpentry(boolvar, buf); (elim) Used terms: pcache[key], boolvar, buf