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Proof step 507 from proof refine-readpage (previous step)

# buf0 = VFS_PAGE_SIZE, asynced ↔ cache_asynced, cache_files[m] = mkfile(m3, md0, # links(m, cache_dirs), content), buf = buf0, dirs = cache_dirs, err = err0, files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, inode = mkinode(m, md, boolvar, m0, m1, m2), 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, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ⟨fail#(; ; err)⟩ (zeropage = buf ∧ ESUCCESS = err), ⟨if pageno ∈ files[inode.ino].content then buf := files[inode.ino].content[pageno] else buf := zeropage; err := ESUCCESS⟩ (zeropage = buf ∧ ESUCCESS = err), datakey(m, pageno) ∈ cache_pcache, pageno ∈ content

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 508:
# buf0 = VFS_PAGE_SIZE, 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), m ∈ cache_files, ¬ pageno ∈ content, ¬ datakey(m, pageno) ∈ cache_pcache, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ⟨fail#(; ; err)⟩ (zeropage = buf0 ∧ ESUCCESS = err), ⟨if pageno ∈ ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m].content then buf0 := ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m].content[pageno] else buf0 := zeropage; err := ESUCCESS⟩ (zeropage = buf0 ∧ ESUCCESS = err)

Rule argument

Additional information

Used simplifier rules: ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)