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

VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, files1[m3] = mkfile(m1, md1, # links(m3, dirs), content0), err = ESUCCESS, pcache = truncate(m3, m2, pcache0), m2 % VFS_PAGE_SIZE ≠ 0, afs-cons(dirs, files1), afs-cons (dirs, files1 [m3, mkfile(m, md, # links(m3, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ]), dcache-cons(dcache, dirs, files1), icache-cons(icache, dirs, files1), pcache-cons(pcache0, dirs, files1), synced(dirs, icache, pcache0), m2 / VFS_PAGE_SIZE ∈ content0, m3 ∈ files1, m2 ≤ m, ¬ datakey(m3, m2 / VFS_PAGE_SIZE) ∈ pcache0, asynced2 → synced(files1, icache, pcache0), ∀ key. key ∈ pcache0 → key.data? ⊦ ⟪pcache_set#(m3, m2 / VFS_PAGE_SIZE, some(fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)).buf, false; err, pcache); if err ≠ ESUCCESS then buf-opt := none⟫ ( icache-cons (icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))], dirs, files1 [m3, mkfile(m, md, # links(m3, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ]) ∧ dcache-cons (dcache, dirs, files1 [m3, mkfile(m, md, # links(m3, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ]) ∧ pcache-cons (pcache, dirs, files1 [m3, mkfile(m, md, # links(m3, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ]) ∧ synced(dirs, icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))], pcache) ∧ ( asynced2 → synced (files1 [m3, mkfile (m, md, # links(m3, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ], icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))], pcache)))

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, files1[m3] = mkfile(m1, md1, # links(m3, dirs), content0), buf = some(fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)).buf, err = ESUCCESS, ino = m3, pageno = m2 / VFS_PAGE_SIZE, pcache = truncate(m3, m2, pcache0), some(fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)).some?, afs-cons (dirs, files1 [m3, mkfile(m, md, # links(m3, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ]), afs-cons(dirs, files1), dcache-cons(dcache, dirs, files1), icache-cons(icache, dirs, files1), pcache-cons(pcache0, dirs, files1), synced(dirs, icache, pcache0), m3 ∈ files1, m2 / VFS_PAGE_SIZE ∈ content0, m2 % VFS_PAGE_SIZE + n0 ≤ # content0[m2 / VFS_PAGE_SIZE], m2 ≤ m, asynced2 → synced(files1, icache, pcache0), ∀ key. key ∈ pcache0 → key.data? ⊦ ⟪let key = datakey(ino, pageno), pe = mkpentry(asynced, buf) in pcache[key] := pe; if err ≠ ESUCCESS then buf-opt := none⟫ ( icache-cons (icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))], dirs, files1 [m3, mkfile(m, md, # links(m3, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ]) ∧ dcache-cons (dcache, dirs, files1 [m3, mkfile(m, md, # links(m3, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ]) ∧ pcache-cons (pcache, dirs, files1 [m3, mkfile(m, md, # links(m3, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ]) ∧ synced(dirs, icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))], pcache) ∧ ( asynced2 → synced (files1 [m3, mkfile (m, md, # links(m3, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ], icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))], pcache))), m2 % VFS_PAGE_SIZE = 0, VFS_PAGE_SIZE = 0, datakey(m3, m2 / VFS_PAGE_SIZE) ∈ 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)