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Proof step 422 from proof refine-truncate (previous step)

# buf-opt0.buf = VFS_PAGE_SIZE, boolvar ↔ m2 ≤ n ∧ pageno0 ≠ 0 ∧ (m2 / VFS_PAGE_SIZE ∈ content ∨ buf-opt0.some?), VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, fs[ri[inodekey(m)]] = inodenode(key, md0, false, m0, 0, m3), abs-files(fs, ri)[m] = mkfile(m1, md1, m4, content0), buf-opt = buf-opt0, content = content0, dirs = abs-dirs(fs, ri), files = abs-files(fs, ri), ino = m, new_inode = mkinode(m, md, false, m0, 0, m2), pageno = min(n, m2), pageno0 = m2 % VFS_PAGE_SIZE, pageno1 = m2 / VFS_PAGE_SIZE, fo.inodes?, orphans(fs, ri).inodes?, buf-opt0.some?, buf-opt.some?, afs-cons(abs-dirs(fs, ri), abs-files(fs, ri)), file-node-cons(fs, ri), log-cons(log, fs), orphans-cons(fs, ri, orphans(fs, ri)), replay-cons-strong(fs, ri, orphans(fs, ri), fi, fo, log), ri-inj(fi), ri-inj(ri), ubifs-cons(fs, ri, orphans(fs, ri), fi, fo, log), inodekey(m) ∈ ri, ri[inodekey(m)] ∈ fs, pageno0 + (VFS_PAGE_SIZE - pageno0) ≤ # buf-opt.buf, m2 ≤ n, VFS_PAGE_SIZE ≥ pageno0, ⌊err1⌋ , m2 ≤ n → pageno0 ≠ 0 → VFS_PAGE_SIZE ≠ 0, asynced → boolvar0 ⊦ ⟨files[ino].content := content[pageno1, fill(buf-opt.buf, zero, pageno0, VFS_PAGE_SIZE - pageno0)] upto pageno; afs_inode_sync#(new_inode.size:= n; dirs, files); inode := (m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ); err := ESUCCESS; asynced := ?⟩ ( dirs = abs-dirs(fs, ri) ∧ files = abs-files(fs, ri) ∧ (asynced → boolvar4) ∧ buf-opt0 = some(fill(buf-opt.buf, zero, pageno0, VFS_PAGE_SIZE - pageno0)) ∧ mkinode(m, md, false, m0, 0, m2) = inode ∧ (boolvar2 ↔ boolvar) ∧ err1 = err), ⟨err := err1; asynced := ?⟩ ((asynced → boolvar4) ∧ err1 = err), m2 % VFS_PAGE_SIZE = 0, VFS_PAGE_SIZE = 0

Heuristic symbolic execution applied rule assign right

And obtained the following new goals

Proof step 423:
# buf-opt0.buf = VFS_PAGE_SIZE, boolvar ↔ m2 ≤ n ∧ pageno0 ≠ 0 ∧ (m2 / VFS_PAGE_SIZE ∈ content ∨ buf-opt0.some?), VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, abs-files(fs, ri)[m] = mkfile(m1, md1, m4, content0), fs[ri[inodekey(m)]] = inodenode(key, md0, false, m0, 0, m3), buf-opt = buf-opt0, content = content0, dirs = abs-dirs(fs, ri), files = files0[ino, files0[ino].content:= (content[pageno1, fill(buf-opt.buf, zero, pageno0, VFS_PAGE_SIZE - pageno0)] upto pageno)], files0 = abs-files(fs, ri), ino = m, new_inode = mkinode(m, md, false, m0, 0, m2), pageno = min(n, m2), pageno0 = m2 % VFS_PAGE_SIZE, pageno1 = m2 / VFS_PAGE_SIZE, orphans(fs, ri).inodes?, fo.inodes?, buf-opt0.some?, buf-opt.some?, afs-cons(abs-dirs(fs, ri), abs-files(fs, ri)), file-node-cons(fs, ri), log-cons(log, fs), orphans-cons(fs, ri, orphans(fs, ri)), replay-cons-strong(fs, ri, orphans(fs, ri), fi, fo, log), ri-inj(ri), ri-inj(fi), ubifs-cons(fs, ri, orphans(fs, ri), fi, fo, log), ri[inodekey(m)] ∈ fs, inodekey(m) ∈ ri, m2 ≤ n, pageno0 + (VFS_PAGE_SIZE - pageno0) ≤ # buf-opt.buf, VFS_PAGE_SIZE ≥ pageno0, ⌊err1⌋ , asynced → boolvar0, m2 ≤ n → pageno0 ≠ 0 → VFS_PAGE_SIZE ≠ 0 ⊦ ⟨afs_inode_sync#(new_inode.size:= n; dirs, files); inode := (m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ); err := ESUCCESS; asynced := ?⟩ ( dirs = abs-dirs(fs, ri) ∧ files = abs-files(fs, ri) ∧ (asynced → boolvar4) ∧ buf-opt0 = some(fill(buf-opt.buf, zero, pageno0, VFS_PAGE_SIZE - pageno0)) ∧ mkinode(m, md, false, m0, 0, m2) = inode ∧ (boolvar2 ↔ boolvar) ∧ err1 = err), ⟨err := err1; asynced := ?⟩ ((asynced → boolvar4) ∧ err1 = err), m2 % VFS_PAGE_SIZE = 0, VFS_PAGE_SIZE = 0

Rule argument

Additional information

Used simplifier rules: ⊦ VFS_PAGE_SIZE ≠ 0; (s)% ⊦ n ≥ m ↔ m ≤ n; (s)%n ≠ 0 ⊦ m % n ≤ n; (s)%n ≤ m ⊦ (m - n) + m0 ≤ n0 ↔ m + m0 ≤ n0 + n; (s)% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic