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Proof step 205 from proof refine-truncate (previous step)

# buf-opt0.buf = VFS_PAGE_SIZE, VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, abs-files (fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, m0, 0, n1)] [adr3, datanode(datakey(m, m2 / VFS_PAGE_SIZE), fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n0)) ], ri0[datakey(m, m2 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2]) [ino ] = mkfile(m1, md1, m4, content), fs0[ri0[inodekey(m)]] = inodenode(key, md0, false, m0, 0, m3), abs-files(fs0, ri0)[m, mkfile(n1, md, m0, abs-content(m, fs0, ri0)[m2 / VFS_PAGE_SIZE, fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2)] = abs-files (fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, m0, 0, n1)] [adr3, datanode(datakey(m, m2 / VFS_PAGE_SIZE), fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n0)) ], ri0[datakey(m, m2 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2] \ datakeys(inodekey(m), m2, ri0[datakey(m, m2 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2])), abs-dirs(fs0, ri0)[ino] = mkdir(m5, md2, m6, m7, entries), abs-dirs(fs0, ri0) = abs-dirs (fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, m0, 0, n1)] [adr3, datanode(datakey(m, m2 / VFS_PAGE_SIZE), fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n0)) ], ri0[datakey(m, m2 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2]), fs0[ri0[inodekey(ROOT_INO)]].directory, orphans(fs0, ri0).inodes?, fo.inodes?, buf-opt0.some?, afs-cons(abs-dirs(fs0, ri0), abs-files(fs0, ri0)), afs-cons (abs-dirs(fs0, ri0), abs-files(fs0, ri0)[m, mkfile(n1, md, m0, abs-content(m, fs0, ri0)[m2 / VFS_PAGE_SIZE, fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2)]), file-node-cons (fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, m0, 0, n1)] [adr3, datanode(datakey(m, m2 / VFS_PAGE_SIZE), fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n0)) ], ri0[datakey(m, m2 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2] \ datakeys(inodekey(m), m2, ri0[datakey(m, m2 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2])), file-node-cons(fs0, ri0), log-cons (log0, fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, m0, 0, n1)] [adr3, datanode(datakey(m, m2 / VFS_PAGE_SIZE), fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n0)) ]), log-cons(log0, fs0), orphans-cons (fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, m0, 0, n1)] [adr3, datanode(datakey(m, m2 / VFS_PAGE_SIZE), fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n0)) ], ri0[datakey(m, m2 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2] \ datakeys(inodekey(m), m2, ri0[datakey(m, m2 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2]), orphans(fs0, ri0)), orphans-cons(fs0, ri0, orphans(fs0, ri0)), replay-cons-strong (fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, m0, 0, n1)] [adr3, datanode(datakey(m, m2 / VFS_PAGE_SIZE), fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n0)) ], ri0[datakey(m, m2 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2] \ datakeys(inodekey(m), m2, ri0[datakey(m, m2 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2]), orphans(fs0, ri0), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), replay-cons-strong(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ri-inj ( ri0[datakey(m, m2 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2] \ datakeys(inodekey(m), m2, ri0[datakey(m, m2 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2])), ri-inj(ri0), ri-inj(fi), ubifs-cons (fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, m0, 0, n1)] [adr3, datanode(datakey(m, m2 / VFS_PAGE_SIZE), fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n0)) ], ri0[datakey(m, m2 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2] \ datakeys(inodekey(m), m2, ri0[datakey(m, m2 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2]), orphans(fs0, ri0), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), inodekey(m) ∈ ri0, ri0[inodekey(m)] ∈ fs0, inodekey(ROOT_INO) ∈ ri0, m2 ≤ n1, asynced0 → boolvar0, inodekey(ino) ∈ ri0 ∧ ¬ fs0[ri0[inodekey(ino)]].directory → fs0[ri0[inodekey(ino)]].nlink = # links(ino, abs-dirs(fs0, ri0)), inodekey(ino) ∈ ri0 ∧ dentrykey(ino, name) ∈ ri0 → inodekey(entries[name]) ∈ ri0 ∧ fs0[ri0[inodekey(entries[name])]].directory ∨ inodekey(entries[name]) ∈ ri0 ∧ ¬ fs0[ri0[inodekey(entries[name])]].directory, inodekey(ino) ∈ ri0 ∧ fs0[ri0[inodekey(ino)]].directory ∧ links(ino, abs-dirs(fs0, ri0)) = ∅ → abs-children(ino, fs0, ri0) = ∅ ⊦ m2 % VFS_PAGE_SIZE = 0, adr1 = adr2, adr1 = adr3, adr2 = adr3, ino = ROOT_INO, m = 0, orphans (abs-dirs(fs0, ri0), abs-files (fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, m0, 0, n1)] [adr3, datanode(datakey(m, m2 / VFS_PAGE_SIZE), fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n0)) ], ri0[datakey(m, m2 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2])) = abs-keys(orphans(fs0, ri0)), adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, inodekey(ino) ∈ ri0 ∧ fs0[ri0[inodekey(ino)]].directory, ( inodekey(ino) ∈ ri0[datakey(m, m2 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2] ∧ ¬ (adr3 = (m = ino ⊃ adr2;ri0[inodekey(ino)]) ⊃ datanode(datakey(m, m2 / VFS_PAGE_SIZE), fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n0)) ;(adr2 = (m = ino ⊃ adr2;ri0[inodekey(ino)]) ⊃ inodenode(inodekey(m), md, false, m0, 0, n1) ;(adr1 = (m = ino ⊃ adr2;ri0[inodekey(ino)]) ⊃ truncnode(inodekey(m), m2);fs0[(m = ino ⊃ adr2;ri0[inodekey(ino)])]) ) ) .directory → (¬ inodekey(ino) ∈ ri0 ∨ ¬ fs0[ri0[inodekey(ino)]].directory) ∧ m4 = # links(ino, abs-dirs(fs0, ri0))) ∧ ( inodekey(ino) ∈ ri0 ∧ fs0[ri0[inodekey(ino)]].directory ∧ dentrykey(ino, name) ∈ ri0 → inodekey(fs0[ri0[dentrykey(ino, name)]].ino) ∈ ri0 ∧ fs0[ri0[inodekey(fs0[ri0[dentrykey(ino, name)]].ino)]].directory ∨ inodekey(fs0[ri0[dentrykey(ino, name)]].ino) ∈ ri0[datakey(m, m2 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2] ∧ ¬ (adr3 = (m = fs0[ri0[dentrykey(ino, name)]].ino ⊃ adr2;ri0[inodekey(fs0[ri0[dentrykey(ino, name)]].ino)]) ⊃ datanode(datakey(m, m2 / VFS_PAGE_SIZE), fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n0)) ;(adr2 = (m = fs0[ri0[dentrykey(ino, name)]].ino ⊃ adr2;ri0[inodekey(fs0[ri0[dentrykey(ino, name)]].ino)]) ⊃ inodenode(inodekey(m), md, false, m0, 0, n1) ;(adr1 = (m = fs0[ri0[dentrykey(ino, name)]].ino ⊃ adr2;ri0[inodekey(fs0[ri0[dentrykey(ino, name)]].ino)]) ⊃ truncnode(inodekey(m), m2) ;fs0[(m = fs0[ri0[dentrykey(ino, name)]].ino ⊃ adr2;ri0[inodekey(fs0[ri0[dentrykey(ino, name)]].ino)])] ) ) ) .directory) ∧ ( inodekey(ino) ∈ ri0[datakey(m, m2 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2] ∧ ¬ (adr3 = (m = ino ⊃ adr2;ri0[inodekey(ino)]) ⊃ datanode(datakey(m, m2 / VFS_PAGE_SIZE), fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n0)) ;(adr2 = (m = ino ⊃ adr2;ri0[inodekey(ino)]) ⊃ inodenode(inodekey(m), md, false, m0, 0, n1) ;(adr1 = (m = ino ⊃ adr2;ri0[inodekey(ino)]) ⊃ truncnode(inodekey(m), m2);fs0[(m = ino ⊃ adr2;ri0[inodekey(ino)])]) ) ) .directory ∧ n ∈ content → # content[n] = VFS_PAGE_SIZE)

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 206:
# buf-opt0.buf = VFS_PAGE_SIZE, VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, abs-dirs(fs0, ri0)[ino] = mkdir(m5, md2, m6, m7, entries), abs-files(fs0, ri0)[m, mkfile(n1, md, m0, abs-content(m, fs0, ri0)[m2 / VFS_PAGE_SIZE, fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2)] = abs-files (fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, m0, 0, n1)] [adr3, datanode(datakey(m, m2 / VFS_PAGE_SIZE), fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n0)) ], ri0[datakey(m, m2 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2] \ datakeys(inodekey(m), m2, ri0[datakey(m, m2 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2])), fs0[ri0[inodekey(m)]] = inodenode(key, md0, false, m0, 0, m3), abs-files (fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, m0, 0, n1)] [adr3, datanode(datakey(m, m2 / VFS_PAGE_SIZE), fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n0)) ], ri0[datakey(m, m2 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2]) [ino ] = mkfile(m1, md1, m4, content), abs-dirs(fs0, ri0) = abs-dirs (fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, m0, 0, n1)] [adr3, datanode(datakey(m, m2 / VFS_PAGE_SIZE), fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n0)) ], ri0[datakey(m, m2 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2]), fs0[ri0[inodekey(ROOT_INO)]].directory, fo.inodes?, orphans(fs0, ri0).inodes?, buf-opt0.some?, afs-cons (abs-dirs(fs0, ri0), abs-files(fs0, ri0)[m, mkfile(n1, md, m0, abs-content(m, fs0, ri0)[m2 / VFS_PAGE_SIZE, fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2)]), afs-cons(abs-dirs(fs0, ri0), abs-files(fs0, ri0)), file-node-cons(fs0, ri0), file-node-cons (fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, m0, 0, n1)] [adr3, datanode(datakey(m, m2 / VFS_PAGE_SIZE), fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n0)) ], ri0[datakey(m, m2 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2] \ datakeys(inodekey(m), m2, ri0[datakey(m, m2 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2])), log-cons(log0, fs0), log-cons (log0, fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, m0, 0, n1)] [adr3, datanode(datakey(m, m2 / VFS_PAGE_SIZE), fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n0)) ]), orphans-cons(fs0, ri0, orphans(fs0, ri0)), orphans-cons (fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, m0, 0, n1)] [adr3, datanode(datakey(m, m2 / VFS_PAGE_SIZE), fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n0)) ], ri0[datakey(m, m2 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2] \ datakeys(inodekey(m), m2, ri0[datakey(m, m2 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2]), orphans(fs0, ri0)), replay-cons-strong(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), replay-cons-strong (fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, m0, 0, n1)] [adr3, datanode(datakey(m, m2 / VFS_PAGE_SIZE), fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n0)) ], ri0[datakey(m, m2 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2] \ datakeys(inodekey(m), m2, ri0[datakey(m, m2 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2]), orphans(fs0, ri0), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), ri-inj(fi), ri-inj(ri0), ri-inj ( ri0[datakey(m, m2 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2] \ datakeys(inodekey(m), m2, ri0[datakey(m, m2 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2])), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ubifs-cons (fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, m0, 0, n1)] [adr3, datanode(datakey(m, m2 / VFS_PAGE_SIZE), fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n0)) ], ri0[datakey(m, m2 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2] \ datakeys(inodekey(m), m2, ri0[datakey(m, m2 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2]), orphans(fs0, ri0), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), inodekey(ROOT_INO) ∈ ri0, ri0[inodekey(m)] ∈ fs0, inodekey(m) ∈ ri0, m2 ≤ n1, inodekey(ino) ∈ ri0 ∧ fs0[ri0[inodekey(ino)]].directory ∧ links(ino, abs-dirs(fs0, ri0)) = ∅ → abs-children(ino, fs0, ri0) = ∅, inodekey(ino) ∈ ri0 ∧ dentrykey(ino, name) ∈ ri0 → inodekey(entries[name]) ∈ ri0 ∧ fs0[ri0[inodekey(entries[name])]].directory ∨ inodekey(entries[name]) ∈ ri0 ∧ ¬ fs0[ri0[inodekey(entries[name])]].directory, inodekey(ino) ∈ ri0 ∧ ¬ fs0[ri0[inodekey(ino)]].directory → fs0[ri0[inodekey(ino)]].nlink = # links(ino, abs-dirs(fs0, ri0)), asynced0 → boolvar0 ⊦ m2 % VFS_PAGE_SIZE = 0, adr1 = adr3, adr1 = adr2, adr2 = adr3, ino = ROOT_INO, m = 0, orphans (abs-dirs(fs0, ri0), abs-files (fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, m0, 0, n1)] [adr3, datanode(datakey(m, m2 / VFS_PAGE_SIZE), fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n0)) ], ri0[datakey(m, m2 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2])) = abs-keys(orphans(fs0, ri0)), adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, dentrykey(ino, name) ∈ ri0, ( inodekey(ino) ∈ ri0[datakey(m, m2 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2] ∧ ¬ (adr3 = (m = ino ⊃ adr2;ri0[inodekey(ino)]) ⊃ datanode(datakey(m, m2 / VFS_PAGE_SIZE), fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n0)) ;(adr2 = (m = ino ⊃ adr2;ri0[inodekey(ino)]) ⊃ inodenode(inodekey(m), md, false, m0, 0, n1) ;(adr1 = (m = ino ⊃ adr2;ri0[inodekey(ino)]) ⊃ truncnode(inodekey(m), m2);fs0[(m = ino ⊃ adr2;ri0[inodekey(ino)])]) ) ) .directory → (¬ inodekey(ino) ∈ ri0 ∨ ¬ fs0[ri0[inodekey(ino)]].directory) ∧ m4 = # links(ino, abs-dirs(fs0, ri0))) ∧ ( inodekey(ino) ∈ ri0 ∧ fs0[ri0[inodekey(ino)]].directory ∧ dentrykey(ino, name) ∈ ri0 → inodekey(fs0[ri0[dentrykey(ino, name)]].ino) ∈ ri0 ∧ fs0[ri0[inodekey(fs0[ri0[dentrykey(ino, name)]].ino)]].directory ∨ inodekey(fs0[ri0[dentrykey(ino, name)]].ino) ∈ ri0[datakey(m, m2 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2] ∧ ¬ (adr3 = (m = fs0[ri0[dentrykey(ino, name)]].ino ⊃ adr2;ri0[inodekey(fs0[ri0[dentrykey(ino, name)]].ino)]) ⊃ datanode(datakey(m, m2 / VFS_PAGE_SIZE), fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n0)) ;(adr2 = (m = fs0[ri0[dentrykey(ino, name)]].ino ⊃ adr2;ri0[inodekey(fs0[ri0[dentrykey(ino, name)]].ino)]) ⊃ inodenode(inodekey(m), md, false, m0, 0, n1) ;(adr1 = (m = fs0[ri0[dentrykey(ino, name)]].ino ⊃ adr2;ri0[inodekey(fs0[ri0[dentrykey(ino, name)]].ino)]) ⊃ truncnode(inodekey(m), m2) ;fs0[(m = fs0[ri0[dentrykey(ino, name)]].ino ⊃ adr2;ri0[inodekey(fs0[ri0[dentrykey(ino, name)]].ino)])] ) ) ) .directory) ∧ ( inodekey(ino) ∈ ri0[datakey(m, m2 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2] ∧ ¬ (adr3 = (m = ino ⊃ adr2;ri0[inodekey(ino)]) ⊃ datanode(datakey(m, m2 / VFS_PAGE_SIZE), fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n0)) ;(adr2 = (m = ino ⊃ adr2;ri0[inodekey(ino)]) ⊃ inodenode(inodekey(m), md, false, m0, 0, n1) ;(adr1 = (m = ino ⊃ adr2;ri0[inodekey(ino)]) ⊃ truncnode(inodekey(m), m2);fs0[(m = ino ⊃ adr2;ri0[inodekey(ino)])]) ) ) .directory ∧ n ∈ content → # content[n] = VFS_PAGE_SIZE), inodekey(ino) ∈ ri0 ∧ fs0[ri0[inodekey(ino)]].directory

Rule argument

fma: dentrykey(ino, name) ∈ ri0

Additional information

Used simplifier rules: ⊦ dentrykey(ino, str) ∈ ri ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → fs[ri[inodekey(ino)]].directory; (ss)% ⊦ ¬ key ∈ ri → ri[key] = (∅)[key]; (s)%ubifs-parent-in: ⊦ dentrykey(ino, str) ∈ ri ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → inodekey(ino) ∈ ri; (forward) from specification aubifs-inv Used formulas: dentrykey(ino, name) ∈ ri0