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Proof step 94 from proof inv-write_inode (previous step)

icache[m] = mkientry(boolvar, mkinode(m1, md1, boolvar0, m3, m4, m5)), dirs[m] = mkdir(m0, md0, # links(m, dirs), m2, entries), afs-cons(dirs[m, mkdir(m0, md, # links(m, dirs), m2, entries)], files), afs-cons(dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), key ∈ pcache, m ∈ icache, m ∈ dirs, asynced2 → synced(files, icache, pcache) ⊦ key.data? ∧ # pcache[key].page = VFS_PAGE_SIZE ∧ key.ino ∈ files ∧ (¬ pcache[key].dirty → key.part ∈ files[key.ino].content ∧ pcache[key].page = files[key.ino].content[key.part])

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 95:
dirs[m] = mkdir(m0, md0, # links(m, dirs), m2, entries), icache[m] = mkientry(boolvar, mkinode(m1, md1, boolvar0, m3, m4, m5)), pcache[key] = mkpentry(boolvar1, buf), afs-cons(dirs, files), afs-cons(dirs[m, mkdir(m0, md, # links(m, dirs), m2, entries)], files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), m ∈ dirs, m ∈ icache, key ∈ pcache, asynced2 → synced(files, icache, pcache) ⊦ key.data? ∧ # buf = VFS_PAGE_SIZE ∧ key.ino ∈ files ∧ (¬ boolvar1 → key.part ∈ files[key.ino].content ∧ buf = 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], boolvar1, buf]

Additional information

Used simplifier rules: ⊦ (boolvar ↔ pe.dirty) ∧ buf = pe.page ↔ pe = mkpentry(boolvar, buf); (elim) Used terms: pcache[key], boolvar1, buf