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Proof step 145 from proof refine-truncate (previous step)

# buf-opt0.buf = VFS_PAGE_SIZE, VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, fs0[ri0[inodekey(m)]] = inodenode(key, md0, false, m0, 0, m3), orphans(fs0, ri0).inodes?, fo.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[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, m2 ≤ n1, asynced0 → boolvar0 ⊦ m2 % VFS_PAGE_SIZE = 0, 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])), adr1 = adr2, adr1 = adr3, adr2 = adr3, m = 0, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 146:
# buf-opt0.buf = VFS_PAGE_SIZE, VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, fs0[ri0[inodekey(m)]] = inodenode(key, md0, false, m0, 0, m3), fo.inodes?, orphans(fs0, ri0).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, 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 '), ri0[inodekey(m)] ∈ fs0, inodekey(m) ∈ ri0, m2 ≤ n1, asynced0 → boolvar0 ⊦ m2 % VFS_PAGE_SIZE = 0, adr1 = adr3, adr1 = adr2, adr2 = adr3, m = 0, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ 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 → (ino = 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) ;mkfile(fs0[ri0[inodekey(ino)]].size, fs0[ri0[inodekey(ino)]].meta, fs0[ri0[inodekey(ino)]].nlink, abs-content(ino, fs0, ri0)) ) = mkfile ((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)])]) ) ) .size, (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)])]) ) ) .meta, (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)])]) ) ) .nlink, abs-content (ino, 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]))))

Rule argument

Additional information

Used simplifier rules: at-ri: ⊦ ri[key, adr][key0] = (key = key0 ⊃ adr;ri[key0]);%⊦ abs-file(ino, fs, ri) = mkfile (fs[ri[inodekey(ino)]].size, fs[ri[inodekey(ino)]].meta, fs[ri[inodekey(ino)]].nlink, abs-content(ino, fs, ri)); (s)%⊦ inodekey(ino) ∈ ri ∧ ¬ fs[ri[inodekey(ino)]].directory → abs-files(fs, ri)[ino] = abs-file(ino, fs, ri); (s)% ⊦ files[ino, af][ino0] = (ino0 = ino ∧ ino ∈ files ⊃ af;files[ino0]); (s)% ⊦ fs[adr0, nd][adr1] = (adr0 = adr1 ⊃ nd;fs[adr1]); (s)% ⊦ inodekey(m) ≠ datakey(m0, m1); (s)% ⊦ inodekey(m) = inodekey(m0) ↔ m = m0; (s)% ⊦ (ri \ ks)[key] = (key ∈ ks ⊃ (∅)[key];ri[key]); (s)% ⊦ ¬ inodekey(m).data?; (s)%⊦ key ∈ datakeys(key0, ri) ↔ key ∈ ri ∧ key.data? ∧ key0.inode? ∧ key.ino = key0.ino; (s)% ⊦ datakeys(key, ri[inodekey(ino), adr]) = datakeys(key, ri); (s)%⊦ key ∈ datakeys(key0, n, ri) ↔ key ∈ datakeys(key0, ri) ∧ n ≤ key.part * VFS_PAGE_SIZE; (s)% ⊦ key ∈ ri \ ks ↔ key ∈ ri ∧ ¬ key ∈ ks; (ls)%⊦ ino ∈ abs-files(fs, ri) ↔ inodekey(ino) ∈ ri ∧ ¬ fs[ri[inodekey(ino)]].directory; (s)% ⊦ ino ∈ files[ino0, af] ↔ ino ∈ files; (s)%⊦ files = abs-files(fs, ri) ↔ (∀ ino. ( ino ∈ files ↔ inodekey(ino) ∈ ri ∧ ¬ fs[ri[inodekey(ino)]].directory) ∧ (ino ∈ files → files[ino] = abs-file(ino, fs, ri))); (ss)