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Proof step 505 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) ⊦ ⟨if pre-readpage(inode, pageno, buf, dirs, files) then { {if pageno ∈ files[inode.ino].content then buf := files[inode.ino].content[pageno] else buf := zeropage; err := ESUCCESS} or fail#(; ; err)} else abort⟩ (zeropage = buf ∧ ESUCCESS = err), datakey(m, pageno) ∈ cache_pcache, pageno ∈ content

Heuristic symbolic execution applied rule if positive right

And obtained the following new goals

Proof step 506:
# 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), 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, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ⟨{if pageno ∈ files[inode.ino].content then buf := files[inode.ino].content[pageno] else buf := zeropage; err := ESUCCESS} or fail#(; ; err)⟩ (zeropage = buf ∧ ESUCCESS = err), pageno ∈ content, datakey(m, pageno) ∈ cache_pcache

Rule argument

Additional information

Used simplifier rules: ⊦ pre-readpage(inode, n, buf, dirs, files) ↔ valid-file-ino(inode.ino, dirs, files) ∧ # buf = VFS_PAGE_SIZE; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)% ⊦ valid-file-ino(ino, dirs, files) ↔ ino ∈ files; (s)% ⊦ ino ∈ files ⊕ icache ↔ ino ∈ files; (s)% ⊦ ino ∈ files ⊕ pcache ↔ ino ∈ files; (s)