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Proof step 449 from proof refine-readpage (previous step)

# buf0 = VFS_PAGE_SIZE, cache_icache[m] = mkientry(boolvar0, mkinode(m2, md1, boolvar, m4, m5, m6)), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m] = mkfile(m0, md, m1, content0), cache_files[m] = mkfile(m3, md0, # links(m, cache_dirs), content), content[pageno] ≠ zeropage, 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, ¬ pageno ∈ content0, ¬ datakey(m, pageno) ∈ cache_pcache, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ∃ err0. ⌊err0⌋ ∧ ⟨err := err0⟩ ( (cache_files ⊕ cache_pcache) ⊕ cache_icache = (cache_files ⊕ cache_pcache[datakey(m, pageno), mkpentry(false, content[pageno])]) ⊕ cache_icache ∧ content[pageno] = buf0 ∧ ESUCCESS = err), m ∈ cache_icache ∧ ¬ boolvar

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 450:
⊦ ino ∈ icache ∧ icache[ino].inode.directory → (files ⊕ icache)[ino] = files[ino]
Proof step 451:
# buf0 = VFS_PAGE_SIZE, cache_files[m] = mkfile(m3, md0, # links(m, cache_dirs), content), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m] = mkfile(m0, md, m1, content0), cache_icache[m] = mkientry(boolvar0, mkinode(m2, md1, boolvar, m4, m5, m6)), 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, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ∃ err0. ⌊err0⌋ ∧ ⟨err := err0⟩ ( (cache_files ⊕ cache_pcache) ⊕ cache_icache = (cache_files ⊕ cache_pcache[datakey(m, pageno), mkpentry(false, content[pageno])]) ⊕ cache_icache ∧ content[pageno] = buf0 ∧ ESUCCESS = err), content[pageno] = zeropage, pageno ∈ content0, datakey(m, pageno) ∈ cache_pcache, m ∈ cache_icache ∧ ¬ boolvar, m ∈ cache_icache ∧ cache_icache[m].inode.directory

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] → [m, cache_icache, cache_files ⊕ cache_pcache] flags: <all paths>

Additional information

Used simplifier rules: ⊦ (files ⊕ pcache)[ino] = mkfile (files[ino].size, files[ino].meta, files[ino].nlink, files[ino].content ⊕ mkcontent(ino, pcache)); (s)%⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0; (ws)% ⊦ mkientry(boolvar, inode).inode = inode; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).directory ↔ boolvar; (s)% ⊦ mkfile(m, md, m0, content).content = content; (s)% ⊦ n ∈ content0 ⊕ content1 ↔ n ∈ content0 ∨ n ∈ content1; (ws) Used terms: m, cache_icache, cache_files ⊕ cache_pcache