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Proof step 22 from proof refine-truncate-buff-some (previous step)

# links(m, cache_dirs) = m5, # buf-opt0.buf = VFS_PAGE_SIZE, asynced0 ↔ asynced5, cache_files[m] = mkfile(m3, md1, m5, content0), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m] = mkfile(m0, md0, m5, content), cache_files[m] = mkfile(m1, md2, m5, content1), afs_dirs = cache_dirs, afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, buf-opt = buf-opt0, err = ESUCCESS, inode = mkinode(m, md, false, m5, 0, m2), m5 = m4, old_ino = 0, size = 0, buf-opt0.some?, 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_truncate_internal#(n, m2 / VFS_PAGE_SIZE; inode, buf-opt, old_ino, size, asynced0, err, cache_dirs, cache_files; asynced); asynced4 := asynced0; if err = ESUCCESS then let asynced = false in {icache_set#(inode, asynced; err, cache_icache); pcache_truncate#(inode.ino, m2, n; err, cache_pcache); if asynced4 then pcache_set#(inode.ino, m2 / VFS_PAGE_SIZE, buf-opt.buf, asynced; err, cache_pcache)}; if (¬ asynced4 ∨ err ≠ ESUCCESS) ∧ ¬ buf-opt0.some? then buf-opt := none⟫ ⟨inode0 := mkinode(m, md, false, m4, 0, m2); afs_truncate#(n, m2 / VFS_PAGE_SIZE; buf-opt0, inode0, asynced5, err0, afs_dirs, afs_files, cache_asynced)⟩ ( afs_dirs = cache_dirs ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (cache_asynced ↔ asynced) ∧ buf-opt = buf-opt0 ∧ inode = inode0 ∧ (asynced4 ↔ asynced5) ∧ err = err0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 23:
# buf-opt0.buf = VFS_PAGE_SIZE, # links(m, cache_dirs) = m4, asynced0 ↔ asynced5, ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m] = mkfile(m0, md0, # links(m, cache_dirs), content), cache_files[m] = mkfile(m1, md2, # links(m, cache_dirs), content1), afs_dirs = cache_dirs, afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, buf-opt = buf-opt0, err = ESUCCESS, inode = mkinode(m, md, false, # links(m, cache_dirs), 0, m2), old_ino = 0, size = 0, buf-opt0.some?, 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) ⊦ ⟪afs_truncate_internal#(n, m2 / VFS_PAGE_SIZE; inode, buf-opt, old_ino, size, asynced0, err, cache_dirs, cache_files; asynced); asynced4 := asynced0; if err = ESUCCESS then let asynced = false in {icache_set#(inode, asynced; err, cache_icache); pcache_truncate#(inode.ino, m2, n; err, cache_pcache); if asynced4 then pcache_set#(inode.ino, m2 / VFS_PAGE_SIZE, buf-opt.buf, asynced; err, cache_pcache)}; if (¬ asynced4 ∨ err ≠ ESUCCESS) ∧ ¬ buf-opt0.some? then buf-opt := none⟫ ⟨inode0 := mkinode(m, md, false, m4, 0, m2); afs_truncate#(n, m2 / VFS_PAGE_SIZE; buf-opt0, inode0, asynced5, err0, afs_dirs, afs_files, cache_asynced)⟩ ( afs_dirs = cache_dirs ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (cache_asynced ↔ asynced) ∧ buf-opt = buf-opt0 ∧ inode = inode0 ∧ (asynced4 ↔ asynced5) ∧ err = err0)

Rule argument

Additional information

Used simplifier rules: ⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0; (ws)