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Proof step 20 from proof refine-writepage (previous step)

# buf = VFS_PAGE_SIZE, cache_files[m] = mkfile(m3, md0, m4, content), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, err = ESUCCESS, 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 ⊦ ⟪pcache_set#(m, pageno, buf, false; 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[m, cache_files[m].content:= content[pageno, buf]] ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ asynced) ∧ err = err0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 21:
# buf = VFS_PAGE_SIZE, cache_files[m] = mkfile(m3, md0, # links(m, cache_dirs), content), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, err = ESUCCESS, 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 ⊦ ⟪pcache_set#(m, pageno, buf, false; 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[m, mkfile(m3, md0, # links(m, cache_dirs), content[pageno, buf])] ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ asynced) ∧ err = err0)

Rule argument

Additional information

Used simplifier rules: ⊦ mkfile(m, md, m0, content).content:= content0 = mkfile(m, md, m0, content0); (s)%afs-cons-file-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, n, content) → # links(ino, dirs) = n; (forward) from specification afs-base