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Proof step 471 from proof refine-readpage (previous step)

# buf0 = VFS_PAGE_SIZE, cache_files[m] = mkfile(m3, md0, # links(m, cache_dirs), content), content[pageno] = zeropage, ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m] = mkfile(m0, md, m1, content0), zeropage ≠ content0[pageno], 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⟩ (content[pageno] = buf0 ∧ ESUCCESS = err)

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 472:
⊦ ino ∈ icache ∧ ¬ icache[ino].inode.directory → (files ⊕ icache)[ino] = mkfile(icache[ino].inode.size, icache[ino].inode.meta, icache[ino].inode.nlink, files[ino].content)
Proof step 473:
# buf0 = VFS_PAGE_SIZE, ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m] = mkfile(m0, md, m1, content0), content[pageno] = zeropage, cache_files[m] = mkfile(m3, md0, # links(m, cache_dirs), content), 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⟩ (content[pageno] = buf0 ∧ ESUCCESS = err), zeropage = content0[pageno], datakey(m, pageno) ∈ cache_pcache, m ∈ cache_icache ∧ ¬ cache_icache[m].inode.directory
Proof step 487:
# buf0 = VFS_PAGE_SIZE, content[pageno] = zeropage, cache_files[m] = mkfile(m3, md0, # links(m, cache_dirs), content), mkfile(cache_icache[m].inode.size, cache_icache[m].inode.meta, cache_icache[m].inode.nlink, (cache_files ⊕ cache_pcache)[m].content) = mkfile(m0, md, m1, 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 ∈ content0, pageno ∈ content, m ∈ cache_files, m ∈ cache_icache, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ∃ err0. ⌊err0⌋ ∧ ⟨err := err0⟩ (content[pageno] = buf0 ∧ ESUCCESS = err), zeropage = content0[pageno], cache_icache[m].inode.directory, datakey(m, pageno) ∈ cache_pcache

Rule argument

spec: cache-base name: at-icache-overwrite seq: ⊦ ino ∈ icache ∧ ¬ icache[ino].inode.directory → (files ⊕ icache)[ino] = mkfile (icache[ino].inode.size, icache[ino].inode.meta, icache[ino].inode.nlink, files[ino].content) 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