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Proof step 133 from proof refine-readpage (previous step)

# buf0 = VFS_PAGE_SIZE, content[pageno] = (content ⊕ mkcontent(m, cache_pcache))[pageno], (∅)[m] = mkientry(boolvar0, mkinode(m2, md1, boolvar, m4, m5, m6)), cache_files[m] = mkfile(m3, md0, # links(m, cache_dirs), content), cache_icache[ino] = mkientry(boolvar2, mkinode(m0, md, boolvar1, m1, m7, m8)), 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), pageno ∈ content ⊕ mkcontent(m, cache_pcache), pageno ∈ content, m ∈ cache_files, ino ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[ino] = ((cache_files ⊕ cache_pcache[datakey(m, pageno), mkpentry(false, content[pageno])]) ⊕ cache_icache)[ino], content[pageno] = zeropage, m ∈ cache_icache, datakey(m, pageno) ∈ cache_pcache, ino ∈ cache_icache ∧ ¬ boolvar1, ino ∈ cache_icache ∧ boolvar1

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 134:
⊦ ¬ ino ∈ icache → (files ⊕ icache)[ino] = files[ino]
Proof step 135:
# buf0 = VFS_PAGE_SIZE, cache_icache[ino] = mkientry(boolvar2, mkinode(m0, md, boolvar1, m1, m7, m8)), cache_files[m] = mkfile(m3, md0, # links(m, cache_dirs), content), (∅)[m] = mkientry(boolvar0, mkinode(m2, md1, boolvar, m4, m5, m6)), content[pageno] = (content ⊕ mkcontent(m, cache_pcache))[pageno], 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), ino ∈ cache_files, m ∈ cache_files, pageno ∈ content, pageno ∈ content ⊕ mkcontent(m, cache_pcache), cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ content[pageno] = zeropage, ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[ino] = (cache_files ⊕ cache_pcache[datakey(m, pageno), mkpentry(false, content[pageno])])[ino], datakey(m, pageno) ∈ cache_pcache, m ∈ cache_icache, ino ∈ cache_icache, ino ∈ cache_icache ∧ boolvar1, ino ∈ cache_icache ∧ ¬ boolvar1

Rule argument

spec: cache-base name: at-icache-overwrite-not-cached seq: ⊦ ¬ ino ∈ icache → (files ⊕ icache)[ino] = files[ino] subst: [ino, icache, files] → [ino, cache_icache, cache_files ⊕ cache_pcache [datakey(m, pageno), mkpentry(false, content[pageno]) ]] flags: <all paths>

Additional information

Used terms: ino, cache_icache, cache_files ⊕ cache_pcache[datakey(m, pageno), mkpentry(false, content[pageno])]