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Proof step 326 from proof refine-readpage (previous step)

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

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 327:
⊦ ino ∈ icache ∧ icache[ino].inode.directory → (files ⊕ icache)[ino] = files[ino]
Proof step 328:
# 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
Proof step 358:
# 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)), cache_icache[ino].inode.directory, 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, ino ∈ cache_icache, 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, ino ∈ cache_icache ∧ ¬ boolvar0

Rule argument

spec: cache-base name: at-icache-overwrite-no-file seq: ⊦ ino ∈ icache ∧ icache[ino].inode.directory → (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])]