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Proof step 71 from proof refine-truncate-buff-some (previous step)

# buf-opt0.buf = VFS_PAGE_SIZE, VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, ((cache_files ⊕ cache_pcache0) ⊕ cache_icache)[m3] = mkfile(m0, md0, # links(m3, cache_dirs), content0), cache_files[m3] = mkfile(m1, md2, # links(m3, cache_dirs), content1), cache_pcache = truncate(m3, m2, cache_pcache0), err = ESUCCESS, m2 % VFS_PAGE_SIZE ≠ 0, buf-opt0.some?, afs-cons(cache_dirs, cache_files), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache0) ⊕ cache_icache), dcache-cons(cache_dcache, cache_dirs, cache_files), icache-cons(cache_icache, cache_dirs, cache_files), pcache-cons(cache_pcache0, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache0), m3 ∈ cache_files, m2 ≤ m, cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data? ⊦ ⟪pcache_set#(m3, m2 / VFS_PAGE_SIZE, some(fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n0)).buf, false; err, cache_pcache); buf-opt1 := some(fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n0)); asynced4 := true; if (¬ asynced4 ∨ err ≠ ESUCCESS) ∧ ¬ buf-opt0.some? then buf-opt1 := none⟫ ⟨inode0 := mkinode(m3, md, false, # links(m3, cache_dirs), 0, m2); cache_dirs0 := cache_dirs; cache_dirs1 := cache_dirs; cache_dirs2 := cache_dirs, buf-opt := buf-opt0; cache_dirs3 := cache_dirs; cache_dirs0 := cache_dirs; cache_dirs1 := cache_dirs; afs_files := (cache_files ⊕ cache_pcache0) ⊕ cache_icache; afs_truncate#(m, m2 / VFS_PAGE_SIZE; buf-opt0, inode0, asynced5, err0, cache_dirs, afs_files, cache_asynced)⟩ ( cache_dirs = cache_dirs3 ∧ afs_files = ( cache_files [m3, mkfile(m, md, # links(m3, cache_dirs2), content1[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ] ⊕ cache_pcache) ⊕ cache_icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, cache_dirs0), 0, m))] ∧ (cache_asynced ↔ asynced0) ∧ buf-opt1 = buf-opt0 ∧ (m3 ∈ cache_dirs1 ⊃ mkinode(m3, cache_dirs1[m3].meta, true, cache_dirs1[m3].nlink, cache_dirs1[m3].nsubdirs, cache_dirs1[m3].size) ;mkinode(m3, md, false, # links(m3, cache_dirs1), 0, m) ) = inode0 ∧ (asynced4 ↔ asynced5) ∧ err = err0)

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 72:
# buf-opt0.buf = VFS_PAGE_SIZE, asynced ↔ false, VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, cache_files[m3] = mkfile(m1, md2, # links(m3, cache_dirs), content1), ((cache_files ⊕ cache_pcache0) ⊕ cache_icache)[m3] = mkfile(m0, md0, # links(m3, cache_dirs), content0), buf = some(fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n0)).buf, cache_pcache = truncate(m3, m2, cache_pcache0), err = ESUCCESS, ino = m3, pageno = m2 / VFS_PAGE_SIZE, pcache = cache_pcache, some(fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n0)).some?, buf-opt0.some?, afs-cons(cache_dirs, (cache_files ⊕ cache_pcache0) ⊕ 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_pcache0, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache0), m3 ∈ cache_files, m2 % VFS_PAGE_SIZE + n0 ≤ # buf-opt0.buf, m2 ≤ m, cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data? ⊦ ⟪let key = datakey(ino, pageno), pe = mkpentry(asynced, buf) in pcache[key] := pe; buf-opt1 := some(fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n0)); asynced4 := true; if (¬ asynced4 ∨ err ≠ ESUCCESS) ∧ ¬ buf-opt0.some? then buf-opt1 := none⟫ ⟨inode0 := mkinode(m3, md, false, # links(m3, cache_dirs), 0, m2); cache_dirs0 := cache_dirs; cache_dirs1 := cache_dirs; cache_dirs2 := cache_dirs, buf-opt := buf-opt0; cache_dirs3 := cache_dirs; cache_dirs0 := cache_dirs; cache_dirs1 := cache_dirs; afs_files := (cache_files ⊕ cache_pcache0) ⊕ cache_icache; afs_truncate#(m, m2 / VFS_PAGE_SIZE; buf-opt0, inode0, asynced5, err0, cache_dirs, afs_files, cache_asynced)⟩ ( cache_dirs = cache_dirs3 ∧ afs_files = ( cache_files [m3, mkfile(m, md, # links(m3, cache_dirs2), content1[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ] ⊕ pcache) ⊕ cache_icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, cache_dirs0), 0, m))] ∧ (cache_asynced ↔ asynced0) ∧ buf-opt1 = buf-opt0 ∧ (m3 ∈ cache_dirs1 ⊃ mkinode(m3, cache_dirs1[m3].meta, true, cache_dirs1[m3].nlink, cache_dirs1[m3].nsubdirs, cache_dirs1[m3].size) ;mkinode(m3, md, false, # links(m3, cache_dirs1), 0, m) ) = inode0 ∧ (asynced4 ↔ asynced5) ∧ err = err0), m2 % VFS_PAGE_SIZE = 0, VFS_PAGE_SIZE = 0

Rule argument

pos: right 1

Additional information

Used simplifier rules: pcache_set#(INO, PAGENO, BUF, DIRTY; ERR, PCACHE) {let KEY = datakey(INO, PAGENO), PE = mkpentry(DIRTY, BUF) in PCACHE[KEY] := PE };% ⊦ some(buf).some?; (s)% ⊦ VFS_PAGE_SIZE ≠ 0; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)%c: ⊦ m + n = n + m; from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic% ⊦ m < n → ¬ n < m; (s)