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Proof step 340 from proof refine-readpage (previous step)

# buf0 = VFS_PAGE_SIZE, (∅)[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], cache_files[ino] = mkfile(m9, md2, # links(ino, cache_dirs), content0), 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) ⊦ content[pageno] = zeropage, datakey(m, pageno) ∈ cache_pcache, ino ∈ cache_icache, (n ∈ content0 ⊕ mkcontent(ino, cache_pcache) ↔ n ∈ content0 ⊕ mkcontent(ino, cache_pcache[datakey(m, pageno), mkpentry(false, content[pageno])])) ∧ ( n ∈ content0 ⊕ mkcontent(ino, cache_pcache) → (content0 ⊕ mkcontent(ino, cache_pcache))[n] = (content0 ⊕ mkcontent(ino, cache_pcache[datakey(m, pageno), mkpentry(false, content[pageno])]))[n])

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 341:
⊦ n ∈ content0 ⊕ content1 ↔ n ∈ content0 ∨ n ∈ content1
Proof step 342:
# buf0 = VFS_PAGE_SIZE, cache_files[ino] = mkfile(m9, md2, # links(ino, cache_dirs), content0), 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)), (∅)[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), ino ∈ cache_files, m ∈ cache_icache, m ∈ cache_files, pageno ∈ content, cache_sync → synced(cache_files, cache_icache, cache_pcache), pageno ∈ content ∨ pageno ∈ mkcontent(m, cache_pcache) ⊦ content[pageno] = zeropage, ino ∈ cache_icache, datakey(m, pageno) ∈ cache_pcache, (n ∈ content0 ⊕ mkcontent(ino, cache_pcache) ↔ n ∈ content0 ⊕ mkcontent(ino, cache_pcache[datakey(m, pageno), mkpentry(false, content[pageno])])) ∧ ( n ∈ content0 ⊕ mkcontent(ino, cache_pcache) → (content0 ⊕ mkcontent(ino, cache_pcache))[n] = (content0 ⊕ mkcontent(ino, cache_pcache[datakey(m, pageno), mkpentry(false, content[pageno])]))[n])

Rule argument

spec: cache-base name: in-overwrite-content seq: ⊦ n ∈ content0 ⊕ content1 ↔ n ∈ content0 ∨ n ∈ content1 subst: [n, content0, content1] → [pageno, content, mkcontent(m, cache_pcache)] flags: <all paths>

Additional information

Used terms: pageno, content, mkcontent(m, cache_pcache)