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Proof step 422 from proof refine-readpage (previous step)

# buf0 = VFS_PAGE_SIZE, cache_icache[m] = mkientry(boolvar0, mkinode(m2, md1, boolvar, m4, m5, m6)), cache_files[m] = mkfile(m3, md0, # links(m, cache_dirs), content), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m] = mkfile(m0, md, m1, content0), content[pageno] ≠ content0[pageno], content[pageno] ≠ zeropage, 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, ¬ 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 423:
⊦ ino ∈ icache ∧ icache[ino].inode.directory → (files ⊕ icache)[ino] = files[ino]
Proof step 424:
# buf0 = VFS_PAGE_SIZE, ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m] = mkfile(m0, md, m1, content0), cache_files[m] = mkfile(m3, md0, # links(m, cache_dirs), content), cache_icache[m] = mkientry(boolvar0, mkinode(m2, md1, boolvar, m4, m5, m6)), 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 ∈ content0, pageno ∈ content, m ∈ cache_files, 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] = content0[pageno], content[pageno] = zeropage, datakey(m, pageno) ∈ cache_pcache, m ∈ cache_icache ∧ ¬ boolvar, m ∈ cache_icache ∧ cache_icache[m].inode.directory
Proof step 430:
# buf0 = VFS_PAGE_SIZE, (cache_files ⊕ cache_pcache)[m] = mkfile(m0, md, m1, content0), cache_files[m] = mkfile(m3, md0, # links(m, cache_dirs), content), cache_icache[m] = mkientry(boolvar0, mkinode(m2, md1, boolvar, m4, m5, m6)), cache_icache[m].inode.directory, 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 ∈ content0, pageno ∈ content, m ∈ cache_files, m ∈ cache_icache, 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] = content0[pageno], content[pageno] = zeropage, datakey(m, pageno) ∈ cache_pcache, m ∈ cache_icache ∧ ¬ boolvar

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 terms: m, cache_icache, cache_files ⊕ cache_pcache