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Proof step 94 from proof refine-truncate-buff-none-uncached (previous step)

VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, ((cache_files ⊕ cache_pcache0) ⊕ cache_icache)[m1] = mkfile(m0, md0, # links(m1, cache_dirs), content0), cache_files[m1] = mkfile(m3, md1, # links(m1, cache_dirs), content), cache_pcache = truncate(m1, m2, cache_pcache0), err = ESUCCESS, m2 % VFS_PAGE_SIZE ≠ 0, 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), m2 / VFS_PAGE_SIZE ∈ content, m1 ∈ cache_files, m2 ≤ m, ¬ datakey(m1, m2 / VFS_PAGE_SIZE) ∈ cache_pcache0, cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data? ⊦ ⟪pcache_set#(m1, m2 / VFS_PAGE_SIZE, some(fill(content[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)).buf, false; err, cache_pcache); buf-opt := some(fill(content[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)); asynced1 := true; if ¬ asynced1 ∨ err ≠ ESUCCESS then buf-opt := none⟫ ⟨buf-opt0 := none; inode0 := mkinode(m1, md, false, # links(m1, cache_dirs), 0, m2); cache_dirs0 := cache_dirs; cache_dirs1 := cache_dirs; cache_dirs2 := cache_dirs; 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 [m1, mkfile (m, md, # links(m1, cache_dirs2), content[m2 / VFS_PAGE_SIZE, fill(content[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ] ⊕ cache_pcache) ⊕ cache_icache[m1, mkientry(false, mkinode(m1, md, false, # links(m1, cache_dirs0), 0, m))] ∧ ¬ cache_asynced ∧ buf-opt = buf-opt0 ∧ (m1 ∈ cache_dirs1 ⊃ mkinode(m1, cache_dirs1[m1].meta, true, cache_dirs1[m1].nlink, cache_dirs1[m1].nsubdirs, cache_dirs1[m1].size) ;mkinode(m1, md, false, # links(m1, cache_dirs1), 0, m) ) = inode0 ∧ (asynced1 ↔ asynced5) ∧ err = err0)

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 95:
asynced ↔ false, VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, cache_files[m1] = mkfile(m3, md1, # links(m1, cache_dirs), content), ((cache_files ⊕ cache_pcache0) ⊕ cache_icache)[m1] = mkfile(m0, md0, # links(m1, cache_dirs), content0), buf = some(fill(content[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)).buf, cache_pcache = truncate(m1, m2, cache_pcache0), err = ESUCCESS, ino = m1, pageno = m2 / VFS_PAGE_SIZE, pcache = cache_pcache, some(fill(content[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)).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), m1 ∈ cache_files, m2 / VFS_PAGE_SIZE ∈ content, m2 % VFS_PAGE_SIZE + n0 ≤ # content[m2 / VFS_PAGE_SIZE], 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-opt := some(fill(content[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)); asynced1 := true; if ¬ asynced1 ∨ err ≠ ESUCCESS then buf-opt := none⟫ ⟨buf-opt0 := none; inode0 := mkinode(m1, md, false, # links(m1, cache_dirs), 0, m2); cache_dirs0 := cache_dirs; cache_dirs1 := cache_dirs; cache_dirs2 := cache_dirs; 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 [m1, mkfile (m, md, # links(m1, cache_dirs2), content[m2 / VFS_PAGE_SIZE, fill(content[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ] ⊕ pcache) ⊕ cache_icache[m1, mkientry(false, mkinode(m1, md, false, # links(m1, cache_dirs0), 0, m))] ∧ ¬ cache_asynced ∧ buf-opt = buf-opt0 ∧ (m1 ∈ cache_dirs1 ⊃ mkinode(m1, cache_dirs1[m1].meta, true, cache_dirs1[m1].nlink, cache_dirs1[m1].nsubdirs, cache_dirs1[m1].size) ;mkinode(m1, md, false, # links(m1, cache_dirs1), 0, m) ) = inode0 ∧ (asynced1 ↔ asynced5) ∧ err = err0), m2 % VFS_PAGE_SIZE = 0, VFS_PAGE_SIZE = 0, datakey(m1, m2 / VFS_PAGE_SIZE) ∈ cache_pcache0

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)%⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, n0, content) ∧ n ∈ content → # content[n] = VFS_PAGE_SIZE; (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)