[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 24 from proof refine-truncate (previous step)

boolvar ↔ true, boolvar3 ↔ boolvar2, boolvar0 ↔ boolvar4, boolvar1 ↔ boolvar3, 0 = fs[ri[inodekey(m)]].nsubdirs, buf-opt = buf-opt0, dirs = abs-dirs(fs, ri), err = ESUCCESS, err1 = err0, files = abs-files(fs, ri), inode = mkinode(m, md, false, fs[ri[inodekey(m)]].nlink, 0, m2), key = datakey(inode.ino, pageno1), key0 = inodekey(inode.ino), key1 = inodekey(inode.ino), m0 = fs[ri[inodekey(m)]].nlink, nd = datanode(key, buf-opt.buf), nd0 = inodenode(key0, inode.meta, inode.directory, inode.nlink, inode.nsubdirs, n), nd1 = truncnode(key1, pageno), pageno = min(n, inode.size), pageno0 = inode.size % VFS_PAGE_SIZE, pageno1 = m2 / VFS_PAGE_SIZE, ro = orphans(fs, ri), ro0 = orphans(fs, ri), nd.data?, fo.inodes?, orphans(fs, ri).inodes?, 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, pageno0 + (VFS_PAGE_SIZE - pageno0) ≤ # nd.data, inode.size ≤ n, VFS_PAGE_SIZE ≥ pageno0, buf-opt0.some? → # buf-opt0.buf = VFS_PAGE_SIZE, asynced → boolvar4 ⊦ [aubifs_core_journal_add3# (nd1, nd0, nd.data:= fill(nd.data, zero, pageno0, VFS_PAGE_SIZE - pageno0), ri, fi, ro, fo; adr1, adr0, adr, fs, log; boolvar0, err); if err = ESUCCESS then aubifs_core_index_store#(key, adr, fi, ro, fo, fs, log, boolvar0; ri); if err = ESUCCESS then {aubifs_core_index_store#(key0, adr0, fi, ro, fo, fs, log, boolvar0; ri); aubifs_core_index_truncate#(key1, pageno, fi, ro, fo, fs, log, boolvar0; ri); boolvar1 := boolvar; inode := mkinode(inode.ino, nd0.meta, nd0.directory, nd0.nlink, nd0.nsubdirs, nd0.size); if boolvar1 then buf-opt := some((nd.data:= fill(nd.data, zero, pageno0, VFS_PAGE_SIZE - pageno0)).data)}] ( ubifs-cons(fs, ri, ro0, fi, fo, log) ∧ replay-cons-strong(fs, ri, ro0, fi, fo, log) ∧ file-node-cons(fs, ri) ∧ orphans-cons(fs, ri, ro0) ∧ ri-inj(ri) ∧ log-cons(log, fs) → ⟨p_inode := mkinode(m, md, false, m0, 0, m2); afs_truncate#(n, m2 / VFS_PAGE_SIZE; buf-opt0, p_inode, boolvar2, err0, dirs, files, asynced)⟩ ( dirs = abs-dirs(fs, ri) ∧ files = abs-files(fs, ri) ∧ orphans(abs-dirs(fs, ri), abs-files(fs, ri)) = abs-keys(ro0) ∧ (asynced → boolvar0) ∧ buf-opt = buf-opt0 ∧ inode = p_inode ∧ (boolvar1 ↔ boolvar2) ∧ err = err0)), VFS_PAGE_SIZE = 0, pageno0 = 0, fs[ri[inodekey(m)]].directory

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 25:
# buf-opt0.buf = VFS_PAGE_SIZE, 0 = fs[ri[inodekey(m)]].nsubdirs, dirs = abs-dirs(fs, ri), files = abs-files(fs, ri), inode = mkinode(m, md, false, fs[ri[inodekey(m)]].nlink, 0, m2), m0 = fs[ri[inodekey(m)]].nlink, ro = orphans(fs, ri), m2 % VFS_PAGE_SIZE ≠ 0, fo.inodes?, orphans(fs, ri).inodes?, buf-opt0.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, m2 ≤ n, ¬ fs[ri[inodekey(m)]].directory, asynced → boolvar4 ⊦ [aubifs_core_journal_add3# (truncnode(inodekey(inode.ino), min(n, inode.size)), inodenode(inodekey(inode.ino), inode.meta, inode.directory, inode.nlink, inode.nsubdirs, n), datanode (datakey(inode.ino, m2 / VFS_PAGE_SIZE), fill (datanode(datakey(inode.ino, m2 / VFS_PAGE_SIZE), buf-opt0.buf).data, zero, inode.size % VFS_PAGE_SIZE, VFS_PAGE_SIZE - inode.size % VFS_PAGE_SIZE)), ri, fi, orphans(fs, ri), fo ; adr1, adr0, adr, fs, log ; boolvar4, err); key := datakey(inode.ino, m2 / VFS_PAGE_SIZE); if err = ESUCCESS then aubifs_core_index_store#(key, adr, fi, ro, fo, fs, log, boolvar4; ri); pageno0 := inode.size % VFS_PAGE_SIZE; nd0 := inodenode(inodekey(inode.ino), inode.meta, inode.directory, inode.nlink, inode.nsubdirs, n); buf-opt := buf-opt0; boolvar3 := boolvar2; if err = ESUCCESS then {aubifs_core_index_store#(inodekey(inode.ino), adr0, fi, ro, fo, fs, log, boolvar4; ri); aubifs_core_index_truncate#(inodekey(inode.ino), min(n, inode.size), fi, ro, fo, fs, log, boolvar4; ri); boolvar3 := true; inode := mkinode(inode.ino, nd0.meta, nd0.directory, nd0.nlink, nd0.nsubdirs, nd0.size); nd := datanode(key, buf-opt.buf); if boolvar3 then buf-opt := some((nd.data:= fill(nd.data, zero, pageno0, VFS_PAGE_SIZE - pageno0)).data)}] ( ubifs-cons(fs, ri, ro, fi, fo, log) ∧ replay-cons-strong(fs, ri, ro, fi, fo, log) ∧ file-node-cons(fs, ri) ∧ orphans-cons(fs, ri, ro) ∧ ri-inj(ri) ∧ log-cons(log, fs) → ⟨p_inode := mkinode(m, md, false, m0, 0, m2); afs_truncate#(n, m2 / VFS_PAGE_SIZE; buf-opt0, p_inode, boolvar2, err0, dirs, files, asynced)⟩ ( dirs = abs-dirs(fs, ri) ∧ files = abs-files(fs, ri) ∧ orphans(abs-dirs(fs, ri), abs-files(fs, ri)) = abs-keys(ro) ∧ (asynced → boolvar4) ∧ buf-opt = buf-opt0 ∧ inode = p_inode ∧ (boolvar3 ↔ boolvar2) ∧ err = err0))

Rule argument

Additional information

Used simplifier rules: ⊦ m ≤ m; (s)% ⊦ datanode(key, buf).data:= buf0 = datanode(key, buf0); (s)% ⊦ datanode(key, buf).data?; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)%n ≤ m ⊦ (m - n) + m0 ≤ n0 ↔ m + m0 ≤ n0 + n; (s)% ⊦ datanode(key, buf).data = buf; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)%n ≠ 0 ⊦ m % n ≤ n; (s)% ⊦ n ≥ m ↔ m ≤ n; (s)% ⊦ VFS_PAGE_SIZE ≠ 0; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).size = m2; (s)