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Proof step 124 from proof refine-readpage (previous step)

# buf0 = VFS_PAGE_SIZE, cache_icache[m] = mkientry(boolvar0, mkinode(m2, md1, boolvar, m4, m5, m6)), content[pageno] = content0[pageno], cache_files[m] = mkfile(m3, md0, # links(m, cache_dirs), content), (cache_files ⊕ cache_pcache)[m] = mkfile(m0, md, m1, content0), 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, pageno ∈ content, pageno ∈ content0, ino ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ content0[pageno] = zeropage, ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[ino] = ((cache_files ⊕ cache_pcache[datakey(m, pageno), mkpentry(false, content0[pageno])]) ⊕ cache_icache)[ino], datakey(m, pageno) ∈ cache_pcache, m ∈ cache_icache, m ∈ cache_icache ∧ boolvar, m ∈ cache_icache ∧ ¬ boolvar

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 125:
# buf0 = VFS_PAGE_SIZE, 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])]) ⊕ cache_icache)[ino], datakey(m, pageno) ∈ cache_pcache, m ∈ cache_icache

Rule argument

Additional information

Used simplifier rules: ⊦ mkfile(m, md, m0, content).content = content; (s)% ⊦ ¬ ino ∈ icache → icache[ino] = (∅)[ino]; (s)%⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0; (ws)%⊦ (files ⊕ pcache)[ino] = mkfile (files[ino].size, files[ino].meta, files[ino].nlink, files[ino].content ⊕ mkcontent(ino, pcache)); (s)