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Proof step 173 from proof inv-writepage (previous step)

# buf = VFS_PAGE_SIZE, afs-cons(dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), key ∈ pcache[datakey(m, pageno), mkpentry(true, buf)], m ∈ files ⊦ key.data? ∧ # pcache[datakey(m, pageno), mkpentry(true, buf)][key].page = VFS_PAGE_SIZE ∧ key.ino ∈ files ∧ ( ¬ pcache[datakey(m, pageno), mkpentry(true, buf)][key].dirty → key.part ∈ files[key.ino].content ∧ pcache[datakey(m, pageno), mkpentry(true, buf)][key].page = files[key.ino].content[key.part])

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 174:
# buf = VFS_PAGE_SIZE, pcache[datakey(m, pageno), mkpentry(true, buf)][key] = mkpentry(boolvar, buf0), afs-cons(dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), m ∈ files, key ∈ pcache[datakey(m, pageno), mkpentry(true, buf)] ⊦ key.data? ∧ # buf0 = VFS_PAGE_SIZE ∧ key.ino ∈ files ∧ (¬ boolvar → key.part ∈ files[key.ino].content ∧ buf0 = 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[datakey(m, pageno), mkpentry(true, buf)][key], boolvar, buf0]

Additional information

Used simplifier rules: ⊦ (boolvar ↔ pe.dirty) ∧ buf = pe.page ↔ pe = mkpentry(boolvar, buf); (elim) Used terms: pcache[datakey(m, pageno), mkpentry(true, buf)][key], boolvar, buf0