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Proof step 13 from proof refine-truncate-buff-none-uncached (previous step)

asynced ↔ asynced5, afs_asynced ↔ cache_asynced, asynced3 ↔ cache_asynced, asynced4 ↔ asynced, asynced2 ↔ buf-opt.some?, asynced1 ↔ false, asynced0 ↔ false, ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m] = mkfile(m0, md0, m1, content), afs_dirs = cache_dirs, afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, buf-opt = none, dirs = cache_dirs, err = ESUCCESS, err1 = err0, files = cache_files, icache = cache_icache, ino = inode.ino, inode = mkinode(m, md, false, m1, 0, m2), pageno = m2 / VFS_PAGE_SIZE, pcache = cache_pcache, size = inode.size, 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), pre-truncate(inode, n, pageno, buf-opt, dirs, files), synced(cache_dirs, cache_icache, cache_pcache), m ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ⟪pcache_check_page#(ino, pageno, pcache; asynced1, asynced0, err); if err = ESUCCESS ∧ asynced1 then pcache_get#(ino, pageno, pcache; asynced1, buf, err); if err = ESUCCESS ∧ asynced1 then buf-opt := some(buf); if err = ESUCCESS then afs_truncate#(n, pageno; buf-opt, inode, asynced4, err, dirs, files, asynced3); if err = ESUCCESS then let asynced = false in {icache_set#(inode, asynced; err, icache); pcache_truncate#(inode.ino, size, n; err, pcache); if asynced4 then pcache_set#(inode.ino, pageno, buf-opt.buf, asynced; err, pcache)}; if (¬ asynced4 ∨ err ≠ ESUCCESS) ∧ ¬ asynced2 then buf-opt := none⟫ ⟨buf-opt0 := none; inode0 := mkinode(m, md, false, m1, 0, m2); afs_truncate#(n, m2 / VFS_PAGE_SIZE; buf-opt0, inode0, asynced5, err0, afs_dirs, afs_files, afs_asynced)⟩ ( afs_dirs = dirs ∧ afs_files = (files ⊕ pcache) ⊕ icache ∧ (afs_asynced ↔ asynced3) ∧ buf-opt = buf-opt0 ∧ inode = inode0 ∧ (asynced4 ↔ asynced5) ∧ err = err0), VFS_PAGE_SIZE = 0, datakey(m, m2 / VFS_PAGE_SIZE) ∈ cache_pcache

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 14:
((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m] = mkfile(m0, md0, cache_files[m].nlink, content), ¬ asynced0, ¬ asynced1, 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), m ∈ cache_files, ¬ datakey(m, m2 / VFS_PAGE_SIZE) ∈ cache_pcache, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ⟪pcache_check_page#(m, m2 / VFS_PAGE_SIZE, cache_pcache; asynced1, asynced0, err); pageno := m2 / VFS_PAGE_SIZE; if err = ESUCCESS ∧ asynced1 then pcache_get#(m, pageno, cache_pcache; asynced1, buf, err); buf-opt := none; if err = ESUCCESS ∧ asynced1 then buf-opt := some(buf); size := m2; inode := mkinode(m, md, false, cache_files[m].nlink, 0, m2); afs_files := (cache_files ⊕ cache_pcache) ⊕ cache_icache; afs_dirs := cache_dirs; afs_asynced := cache_asynced; asynced := asynced5; m1 := cache_files[m].nlink; if err = ESUCCESS then afs_truncate#(n, pageno; buf-opt, inode, asynced, err, cache_dirs, cache_files, cache_asynced); if err = ESUCCESS then let asynced0 = false in {icache_set#(inode, asynced0; err, cache_icache); pcache_truncate#(inode.ino, size, n; err, cache_pcache); if asynced then pcache_set#(inode.ino, pageno, buf-opt.buf, asynced0; err, cache_pcache)}; if ¬ asynced ∨ err ≠ ESUCCESS then buf-opt := none⟫ ⟨buf-opt0 := none; inode0 := mkinode(m, md, false, m1, 0, m2); afs_truncate#(n, m2 / VFS_PAGE_SIZE; buf-opt0, inode0, asynced5, err0, afs_dirs, afs_files, afs_asynced)⟩ ( afs_dirs = cache_dirs ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ cache_asynced) ∧ buf-opt = buf-opt0 ∧ inode = inode0 ∧ (asynced ↔ asynced5) ∧ err = err0)

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ none.some?; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).size = m2; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).directory ↔ boolvar; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nsubdirs = m1; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nlink = m0; (s)% ⊦ valid-file-ino(ino, dirs, files) ↔ ino ∈ files; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)%⊦ valid-file-inode(inode, dirs, files) ↔ valid-file-ino(inode.ino, dirs, files) ∧ inode.nlink = files[inode.ino].nlink ∧ inode.nsubdirs = 0 ∧ ¬ inode.directory; (s)%⊦ pre-truncate(inode, n, pageno, buf-opt, dirs, files) ↔ valid-file-inode(inode, dirs, files) ∧ pageno = inode.size / VFS_PAGE_SIZE ∧ (buf-opt.some? → # buf-opt.buf = VFS_PAGE_SIZE); (s)% ⊦ VFS_PAGE_SIZE ≠ 0; (s)