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Proof step 17 from proof refine-truncate-buff-some (previous step)

# links(m, cache_dirs) = m4, # buf-opt0.buf = VFS_PAGE_SIZE, asynced3 ↔ cache_asynced, asynced4 ↔ asynced5, ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m] = mkfile(m0, md0, # links(m, cache_dirs), content), cache_files[m] = mkfile(m3, md1, # links(m, cache_dirs), content0), 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), 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#(n, m2 / VFS_PAGE_SIZE; buf-opt, inode, asynced4, err, cache_dirs, cache_files, asynced3); 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 ↔ asynced3) ∧ buf-opt = buf-opt0 ∧ inode = inode0 ∧ (asynced4 ↔ asynced5) ∧ err = err0)

User applied rule call right

And obtained the following new goals

Proof step 18:
# buf-opt0.buf = VFS_PAGE_SIZE, # links(m, cache_dirs) = m4, asynced0 ↔ asynced4, asynced ↔ asynced3, asynced4 ↔ asynced5, asynced3 ↔ cache_asynced, cache_files[m] = mkfile(m3, md1, # links(m, cache_dirs), content0), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m] = mkfile(m0, md0, # links(m, cache_dirs), content), afs_dirs = cache_dirs, afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, buf-opt = buf-opt0, dirs = cache_dirs, err = ESUCCESS, files = cache_files, inode = mkinode(m, md, false, # links(m, cache_dirs), 0, m2), pageno = m2 / VFS_PAGE_SIZE, 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) ⊦ ⟪if pre-truncate(inode, n, pageno, buf-opt, dirs, files) then let old_ino = 0, size = 0 in afs_truncate_internal#(n, pageno; inode, buf-opt, old_ino, size, asynced0, err, dirs, files; asynced) else abort; 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 = dirs ∧ afs_files = (files ⊕ cache_pcache) ⊕ cache_icache ∧ (cache_asynced ↔ asynced) ∧ buf-opt = buf-opt0 ∧ inode = inode0 ∧ (asynced4 ↔ asynced5) ∧ err = err0), VFS_PAGE_SIZE = 0

Rule argument

pos: right 1

Additional information

Used simplifier rules: afs_truncate# (N, PAGENO; PBUF-OPT, INODE, MODIFIED, ERR, DIRS, FILES, ASYNCED) {if pre-truncate(INODE, N, PAGENO, PBUF-OPT, DIRS, FILES) then let OFFSET = 0, SIZE = 0 in afs_truncate_internal# (N, PAGENO ; INODE, PBUF-OPT, OFFSET, SIZE, MODIFIED, ERR, DIRS, FILES ; ASYNCED) else abort };% ⊦ VFS_PAGE_SIZE ≠ 0; (s)