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Proof step 20 from proof refine-readpage (previous step)

# buf0 = VFS_PAGE_SIZE, afs-cons(cache_dirs, cache_files), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), dcache-cons(cache_dcache, cache_dirs, cache_files), icache-cons(cache_icache, cache_dirs, cache_files), pcache-cons(cache_pcache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache), datakey(m, pageno) ∈ cache_pcache, m ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ⟨afs_readpage#(mkinode(m, md, boolvar, m0, m1, m2), pageno, cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache, cache_asynced; buf0, err0)⟩ (cache_pcache[datakey(m, pageno)].page = buf0 ∧ ESUCCESS = err0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 21:
# buf0 = VFS_PAGE_SIZE, cache_pcache[datakey(m, pageno)] = mkpentry(boolvar0, buf), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), afs-cons(cache_dirs, cache_files), dcache-cons(cache_dcache, cache_dirs, cache_files), icache-cons(cache_icache, cache_dirs, cache_files), pcache-cons(cache_pcache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache), m ∈ cache_files, datakey(m, pageno) ∈ cache_pcache, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ⟨afs_readpage#(mkinode(m, md, boolvar, m0, m1, m2), pageno, cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache, cache_asynced; buf0, err0)⟩ (buf = buf0 ∧ ESUCCESS = err0)

Rule argument

spec: pcache-entry name: elim seq: ⊦ (boolvar ↔ pe.dirty) ∧ buf = pe.page ↔ pe = mkpentry(boolvar, buf) subst: [pe, boolvar, buf] → [cache_pcache[datakey(m, pageno)], boolvar0, buf]

Additional information

Used simplifier rules: ⊦ (boolvar ↔ pe.dirty) ∧ buf = pe.page ↔ pe = mkpentry(boolvar, buf); (elim) Used terms: cache_pcache[datakey(m, pageno)], boolvar0, buf