| # 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 ∈ content, m ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ∃ err0. ⌊err0⌋ ∧ ⟨err := err0⟩ (content[pageno] = buf0 ∧ ESUCCESS = err), ⟨if pageno ∈ content0 then buf0 := content0[pageno] else buf0 := zeropage; err := ESUCCESS⟩ (content[pageno] = buf0 ∧ ESUCCESS = err), datakey(m, pageno) ∈ cache_pcache |
# 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), 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, ¬ datakey(m, pageno) ∈ cache_pcache, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ∃ err0. ⌊err0⌋ ∧ ⟨err := err0⟩ (content[pageno] = buf0 ∧ ESUCCESS = err), ⟨if pageno ∈ content0 then buf0 := content0[pageno] else buf0 := zeropage; err := ESUCCESS⟩ (content[pageno] = buf0 ∧ ESUCCESS = err)