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Proof step 405 from proof refine-readpage (previous step)

# buf0 = VFS_PAGE_SIZE, cache_files[ino] = mkfile(m9, md2, # links(ino, cache_dirs), content0), 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_icache[ino] = mkientry(boolvar0, mkinode(m5, md1, false, m6, 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), ino ∈ cache_icache, pageno ∈ content, m ∈ cache_files, m ∈ cache_icache, ino ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ n ∈ content0 ⊕ mkcontent(ino, cache_pcache) ↔ n ∈ content0 ∨ datakey(ino, n) ∈ cache_pcache[datakey(m, pageno), mkpentry(false, content[pageno])], content[pageno] = zeropage, datakey(m, pageno) ∈ cache_pcache

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 406:
⊦ key ∈ pcache[key0, pe] ↔ key = key0 ∨ key ∈ pcache

Rule argument

spec: store, inst: pcache name: In-insert seq: ⊦ key ∈ pcache[key0, pe] ↔ key = key0 ∨ key ∈ pcache subst: [pe, key0, pcache, key] → [mkpentry(false, content[pageno]), datakey(m, pageno), cache_pcache, datakey(ino, n)] flags: <all paths>

Additional information

Used simplifier rules: ⊦ n ∈ content0 ⊕ content1 ↔ n ∈ content0 ∨ n ∈ content1; (ws)% ⊦ n ∈ mkcontent(ino, pcache) ↔ datakey(ino, n) ∈ pcache; (s)% ⊦ datakey(m, m0) = datakey(m1, m2) ↔ m = m1 ∧ m0 = m2; (ws)%⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0; (ws) Used terms: mkpentry(false, content[pageno]), datakey(m, pageno), cache_pcache, datakey(ino, n)