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Proof step 328 from proof refine-readpage (previous step)

# buf0 = VFS_PAGE_SIZE, content[pageno] = (content ⊕ mkcontent(m, cache_pcache))[pageno], cache_files[m] = mkfile(m3, md0, # links(m, cache_dirs), content), cache_icache[m] = mkientry(boolvar, mkinode(m0, md, false, m1, m2, m4)), cache_icache[ino] = mkientry(boolvar1, mkinode(m5, md1, boolvar0, m6, m7, m8)), 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), pageno ∈ content ⊕ mkcontent(m, cache_pcache), ino ∈ cache_files, m ∈ cache_icache, m ∈ cache_files, pageno ∈ content, 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])]) ⊕ cache_icache)[ino], datakey(m, pageno) ∈ cache_pcache, ino ∈ cache_icache ∧ ¬ boolvar0, ino ∈ cache_icache ∧ cache_icache[ino].inode.directory

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 329:
# buf0 = VFS_PAGE_SIZE, content[pageno] = (content ⊕ mkcontent(m, cache_pcache))[pageno], cache_files[m] = mkfile(m3, md0, # links(m, cache_dirs), content), cache_icache[m] = mkientry(boolvar, mkinode(m0, md, false, m1, m2, m4)), cache_icache[ino] = mkientry(boolvar1, mkinode(m5, md1, boolvar0, m6, m7, m8)), 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), pageno ∈ content ⊕ mkcontent(m, cache_pcache), ino ∈ cache_files, m ∈ cache_icache, m ∈ cache_files, pageno ∈ content, 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])]) ⊕ cache_icache)[ino], datakey(m, pageno) ∈ cache_pcache, ino ∈ cache_icache ∧ ¬ boolvar0, ino ∈ cache_icache ∧ boolvar0

Rule argument

Additional information

Used simplifier rules: ⊦ mkinode(m, md, boolvar, m0, m1, m2).directory ↔ boolvar; (s)% ⊦ mkientry(boolvar, inode).inode = inode; (s)