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Proof step 6 from proof refine-writepage (previous step)

# buf = VFS_PAGE_SIZE, asynced1 ↔ cache_sync, asynced0 ↔ cache_asynced, afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, dirs = cache_dirs, err = err0, files = cache_files, inode = mkinode(m, md, boolvar, m0, m1, m2), pcache = cache_pcache, 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 pre-writepage(inode, pageno, buf, dirs, files) then let asynced = true in {if asynced1 then {afs_writepage#(inode, pageno, buf, dirs; err, files; asynced0); asynced := false} else err := ESUCCESS; if err = ESUCCESS then pcache_set#(inode.ino, pageno, buf, asynced; err, pcache)} else abort⟫ ⟨afs_writepage#(mkinode(m, md, boolvar, m0, m1, m2), pageno, buf, cache_dirs; err0, afs_files; afs_asynced)⟩ (afs_files = (files ⊕ pcache) ⊕ cache_icache ∧ (afs_asynced ↔ asynced0) ∧ err = err0)

Heuristic symbolic execution applied rule if positive right

And obtained the following new goals

Proof step 7:
# buf = VFS_PAGE_SIZE, asynced0 ↔ cache_asynced, asynced1 ↔ cache_sync, afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, dirs = cache_dirs, err = err0, files = cache_files, inode = mkinode(m, md, boolvar, m0, m1, m2), pcache = cache_pcache, 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) ⊦ ⟪let asynced = true in {if asynced1 then {afs_writepage#(inode, pageno, buf, dirs; err, files; asynced0); asynced := false} else err := ESUCCESS; if err = ESUCCESS then pcache_set#(inode.ino, pageno, buf, asynced; err, pcache)}⟫ ⟨afs_writepage#(mkinode(m, md, boolvar, m0, m1, m2), pageno, buf, cache_dirs; err0, afs_files; afs_asynced)⟩ (afs_files = (files ⊕ pcache) ⊕ cache_icache ∧ (afs_asynced ↔ asynced0) ∧ err = err0)

Rule argument

pos: right 1

Additional information

Used simplifier rules: ⊦ pre-writepage(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)