[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 480 from proof refine-truncate (previous step)

boolvar ↔ boolvar4, boolvar1 ↔ boolvar2, VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, fs0[ri0[datakey(m, m2 / VFS_PAGE_SIZE)]] = datanode(key0, buf), fs0[ri0[inodekey(m)]] = inodenode(key1, md0, false, m3, 0, m5), adr = adr3, buf-opt = buf-opt0, dirs = abs-dirs(fs0, ri0), err = ESUCCESS, files = abs-files(fs0, ri0), fs = fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, m3, 0, n)] [adr3, datanode(key0, buf).data:= fill(buf, zero, m2 % VFS_PAGE_SIZE, n0) ], fs1 = fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, m3, 0, n)] [adr3, datanode(key0, buf).data:= fill(buf, zero, m2 % VFS_PAGE_SIZE, n0) ], inode = mkinode(m, md, false, m3, 0, m2), key = datakey(m, m2 / VFS_PAGE_SIZE), log = ((log0 + adr1 ') + adr2 ') + adr3 ', log1 = ((log0 + adr1 ') + adr2 ') + adr3 ', ri = ri0[key, adr], ro = orphans(fs0, ri0), ro0 = orphans(fs0, ri0), datanode(key0, buf).data?, key0.data?, fo.inodes?, orphans(fs0, ri0).inodes?, afs-cons(abs-dirs(fs0, ri0), abs-files(fs0, ri0)), file-node-cons(fs0, ri0), key-cons(key, fs1[adr]), log-cons(log0, fs0), orphans-cons(fs0, ri0, orphans(fs0, ri0)), replay-cons-strong(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ri-cons(ri0, fs0), ri-inj(fi), ri-inj(ri0), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), datakey(m, m2 / VFS_PAGE_SIZE) ∈ ri0, ri0[datakey(m, m2 / VFS_PAGE_SIZE)] ∈ fs0, ri0[inodekey(m)] ∈ fs0, inodekey(m) ∈ ri0, adr ∈ fs1, m2 % VFS_PAGE_SIZE + n0 ≤ # buf, m2 ≤ n, m2 % VFS_PAGE_SIZE + n0 ≤ # datanode(key0, buf).data, asynced → boolvar0, ¬ adr ∈ ri0 → adr ∈ fs1 → adr ∈ fs1 ⊦ [aubifs_core_index_store#(inodekey(m), adr2, fi, ro0, fo, fs, log, boolvar4; ri); aubifs_core_index_truncate#(inodekey(m), min(n, m2), fi, ro0, fo, fs, log, boolvar4; ri); boolvar1 := true; inode := mkinode (inode.ino, inodenode(inodekey(m), md, false, m3, 0, n).meta, inodenode(inodekey(m), md, false, m3, 0, n).directory, inodenode(inodekey(m), md, false, m3, 0, n).nlink, inodenode(inodekey(m), md, false, m3, 0, n).nsubdirs, inodenode(inodekey(m), md, false, m3, 0, n).size); if boolvar1 then buf-opt := some(datanode(key0, fill(datanode(key0, buf).data, zero, m2 % VFS_PAGE_SIZE, n0)).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, m3, 0, m2); afs_truncate#(n, m2 / VFS_PAGE_SIZE; buf-opt0, p_inode, boolvar2, err1, 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 → boolvar4) ∧ buf-opt = buf-opt0 ∧ inode = p_inode ∧ (boolvar1 ↔ boolvar2) ∧ err = err1)), m2 % VFS_PAGE_SIZE = 0, VFS_PAGE_SIZE = 0, adr1 = adr2, adr1 = adr3, adr2 = adr3, m = 0, buf-opt0.some?, adr ∈ ri0, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 481:
VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, fs0[ri0[inodekey(m)]] = inodenode(key1, md0, false, m3, 0, m5), fs0[ri0[datakey(m, m2 / VFS_PAGE_SIZE)]] = datanode(datakey(m, m2 / VFS_PAGE_SIZE), buf), ri = ri0[datakey(m, m2 / VFS_PAGE_SIZE), adr3], m2 % VFS_PAGE_SIZE ≠ 0, adr1 ≠ adr3, adr1 ≠ adr2, adr2 ≠ adr3, m ≠ 0, orphans(fs0, ri0).inodes?, fo.inodes?, afs-cons(abs-dirs(fs0, ri0), abs-files(fs0, ri0)), file-node-cons(fs0, ri0), log-cons(log0, fs0), orphans-cons(fs0, ri0, orphans(fs0, ri0)), replay-cons-strong(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ri-cons(ri0, fs0), ri-inj(ri0), ri-inj(fi), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ri0[inodekey(m)] ∈ fs0, ri0[datakey(m, m2 / VFS_PAGE_SIZE)] ∈ fs0, datakey(m, m2 / VFS_PAGE_SIZE) ∈ ri0, inodekey(m) ∈ ri0, m2 ≤ n, VFS_PAGE_SIZE ≤ # buf, ¬ buf-opt0.some?, ¬ adr1 ∈ fs0, ¬ adr2 ∈ fs0, ¬ adr3 ∈ fs0, ¬ adr3 ∈ ri0, asynced → boolvar0 ⊦ [aubifs_core_index_store# (inodekey(m), adr2, fi, orphans(fs0, ri0), fo, fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, m3, 0, n)] [adr3, datanode(datakey(m, m2 / VFS_PAGE_SIZE), buf).data:= fill(buf, zero, m2 % VFS_PAGE_SIZE, n0) ], ((log0 + adr1 ') + adr2 ') + adr3 ', boolvar4 ; ri); aubifs_core_index_truncate# (inodekey(m), min(n, m2), fi, orphans(fs0, ri0), fo, fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, m3, 0, n)] [adr3, datanode(datakey(m, m2 / VFS_PAGE_SIZE), buf).data:= fill(buf, zero, m2 % VFS_PAGE_SIZE, n0) ], ((log0 + adr1 ') + adr2 ') + adr3 ', boolvar4 ; ri); boolvar1 := true; inode := mkinode (m, inodenode(inodekey(m), md, false, m3, 0, n).meta, inodenode(inodekey(m), md, false, m3, 0, n).directory, inodenode(inodekey(m), md, false, m3, 0, n).nlink, inodenode(inodekey(m), md, false, m3, 0, n).nsubdirs, inodenode(inodekey(m), md, false, m3, 0, n).size); buf-opt := buf-opt0; key0 := datakey(m, m2 / VFS_PAGE_SIZE); if boolvar1 then buf-opt := some(datanode(key0, fill(datanode(key0, buf).data, zero, m2 % VFS_PAGE_SIZE, n0)).data)] ( ubifs-cons (fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, m3, 0, n)] [adr3, datanode(key0, fill(buf, zero, m2 % VFS_PAGE_SIZE, n0)) ], ri, orphans(fs0, ri0), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 ') ∧ replay-cons-strong (fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, m3, 0, n)] [adr3, datanode(key0, fill(buf, zero, m2 % VFS_PAGE_SIZE, n0)) ], ri, orphans(fs0, ri0), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 ') ∧ file-node-cons (fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, m3, 0, n)] [adr3, datanode(key0, fill(buf, zero, m2 % VFS_PAGE_SIZE, n0)) ], ri) ∧ orphans-cons (fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, m3, 0, n)] [adr3, datanode(key0, fill(buf, zero, m2 % VFS_PAGE_SIZE, n0)) ], ri, orphans(fs0, ri0)) ∧ ri-inj(ri) ∧ log-cons (log0, fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, m3, 0, n)] [adr3, datanode(key0, fill(buf, zero, m2 % VFS_PAGE_SIZE, n0)) ]) → ⟨p_inode := mkinode(m, md, false, m3, 0, m2); files := abs-files(fs0, ri0); dirs := abs-dirs(fs0, ri0); afs_truncate#(n, m2 / VFS_PAGE_SIZE; buf-opt0, p_inode, boolvar2, err1, dirs, files, asynced)⟩ ( dirs = abs-dirs (fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, m3, 0, n)] [adr3, datanode(key0, fill(buf, zero, m2 % VFS_PAGE_SIZE, n0)) ], ri) ∧ files = abs-files (fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, m3, 0, n)] [adr3, datanode(key0, fill(buf, zero, m2 % VFS_PAGE_SIZE, n0)) ], ri) ∧ orphans (abs-dirs (fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, m3, 0, n)] [adr3, datanode(key0, fill(buf, zero, m2 % VFS_PAGE_SIZE, n0)) ], ri), abs-files (fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, m3, 0, n)] [adr3, datanode(key0, fill(buf, zero, m2 % VFS_PAGE_SIZE, n0)) ], ri)) = abs-keys(orphans(fs0, ri0)) ∧ (asynced → boolvar4) ∧ buf-opt = buf-opt0 ∧ inode = p_inode ∧ (boolvar1 ↔ boolvar2) ∧ ESUCCESS = err1))

Rule argument

Additional information

Used simplifier rules: ⊦ inodenode(key, md, boolvar, m, m0, m1).directory ↔ boolvar; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).inode?; (s)% ⊦ datakey(m, m0).data?; (s)%ubifs-file-in: ⊦ datakey(ino, n) ∈ ri ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → inodekey(ino) ∈ ri; (forward) from specification aubifs-inv%ubifs-file-notdir: ⊦ datakey(ino, n) ∈ ri ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → ¬ fs[ri[inodekey(ino)]].directory; (forward) from specification aubifs-inv%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[address-list-set]% ⊦ node-cons(key0, datanode(key1, buf)) ↔ key0.data?; (s)% ⊦ inodekey(m).ino = m; (s)%⊦ node-cons(key0, inodenode(key1, md, boolvar, n, n0, m)) ↔ key0.inode? ∧ key0.ino ≠ 0; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).key = key; (s)% ⊦ inodekey(m).inode?; (s)% ⊦ node-cons(key0, truncnode(key1, n)) ↔ key0.inode?; (s)% ⊦ truncnode(key, m).key = key; (s)% ⊦ adr ≠ adr0 → fs[adr0, nd][adr] = fs[adr]; (s)% ⊦ adr ∈ fs[adr0, nd] ↔ adr = adr0 ∨ adr ∈ fs; (ws)% ⊦ adr ≠ adr0 → (adr ∈ fs[adr0, nd] ↔ adr ∈ fs); (s)% ⊦ log-cons(adr ', fs) ↔ adr ∈ fs ∧ node-cons(fs[adr].key, fs[adr]); (s)% ⊦ log-cons(log0 + log1, fs) ↔ log-cons(log0, fs) ∧ log-cons(log1, fs); (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)% ⊦ datanode(key, buf).key = key; (s)% ⊦ datanode(key, buf).data?; (s)% ⊦ key-cons(datakey(ino, n), nd) ↔ nd.data? ∧ nd.key = datakey(ino, n); (s)% ⊦ fs[adr0, nd][adr1] = (adr0 = adr1 ⊃ nd;fs[adr1]); (s)% ⊦ adr ∈ fs[adr1, nd] ↔ adr = adr1 ∨ adr ∈ fs; (s)% ⊦ datanode(key, buf).data:= buf0 = datanode(key, buf0); (s)% ⊦ datanode(key, buf).data = buf; (s)% ⊦ VFS_PAGE_SIZE ≠ 0; (s)