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Proof step 9 from proof refine-writepage (previous step)

# buf = VFS_PAGE_SIZE, asynced0 ↔ cache_asynced, asynced1 ↔ cache_sync, asynced ↔ true, afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, asynced1, 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) ⊦ ⟪afs_writepage#(inode, pageno, buf, dirs; err, files; asynced0); asynced := false; 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)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
# buf = VFS_PAGE_SIZE, afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, err = err0, 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), synced(cache_files, cache_icache, cache_pcache), m ∈ cache_files ⊦ ⟪afs_writepage#(mkinode(m, md, boolvar, m0, m1, m2), pageno, buf, cache_dirs; err, cache_files; asynced0); asynced := false; if err = ESUCCESS then pcache_set#(m, pageno, buf, asynced; err, cache_pcache)⟫ ⟨afs_writepage#(mkinode(m, md, boolvar, m0, m1, m2), pageno, buf, cache_dirs; err0, afs_files; afs_asynced)⟩ (afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ asynced0) ∧ err = err0)

Rule argument

Additional information

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