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Proof step 1357 from proof refine-truncate (previous step)

abs-files(fs0, ri0)[m, mkfile(n0, md, m0, abs-content(m, fs0, ri0) upto min(n0, m2))] = abs-files (fs0[adr1, truncnode(inodekey(m), min(n0, m2))][adr2, inodenode(inodekey(m), md, false, m0, 0, n0)], ri0[inodekey(m), adr2] \ datakeys(inodekey(m), min(n0, m2), ri0[inodekey(m), adr2])), fs0[ri0[inodekey(m)]] = inodenode(key, md0, false, m0, 0, m3), abs-dirs(fs0, ri0) = abs-dirs(fs0[adr1, truncnode(inodekey(m), min(n0, m2))][adr2, inodenode(inodekey(m), md, false, m0, 0, n0)], ri0[inodekey(m), adr2]), fo.inodes?, orphans(fs0, ri0).inodes?, afs-cons(abs-dirs(fs0, ri0), abs-files(fs0, ri0)), afs-cons(abs-dirs(fs0, ri0), abs-files(fs0, ri0)[m, mkfile(n0, md, m0, abs-content(m, fs0, ri0) upto min(n0, m2))]), file-node-cons(fs0, ri0), file-node-cons (fs0[adr1, truncnode(inodekey(m), min(n0, m2))][adr2, inodenode(inodekey(m), md, false, m0, 0, n0)], ri0[inodekey(m), adr2] \ datakeys(inodekey(m), min(n0, m2), ri0[inodekey(m), adr2])), log-cons(log0, fs0), orphans-cons(fs0, ri0, orphans(fs0, ri0)), orphans-cons (fs0[adr1, truncnode(inodekey(m), min(n0, m2))][adr2, inodenode(inodekey(m), md, false, m0, 0, n0)], ri0[inodekey(m), adr2] \ datakeys(inodekey(m), min(n0, m2), ri0[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), min(n0, m2))][adr2, inodenode(inodekey(m), md, false, m0, 0, n0)], ri0[inodekey(m), adr2] \ datakeys(inodekey(m), min(n0, m2), ri0[inodekey(m), adr2]), orphans(fs0, ri0), fi, fo, (log0 + adr1 ') + adr2 '), ri-inj(fi), ri-inj(ri0), ri-inj(ri0[inodekey(m), adr2] \ datakeys(inodekey(m), min(n0, m2), ri0[inodekey(m), adr2])), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ubifs-cons (fs0[adr1, truncnode(inodekey(m), min(n0, m2))][adr2, inodenode(inodekey(m), md, false, m0, 0, n0)], ri0[inodekey(m), adr2] \ datakeys(inodekey(m), min(n0, m2), ri0[inodekey(m), adr2]), orphans(fs0, ri0), fi, fo, (log0 + adr1 ') + adr2 '), inodekey(m) ∈ ri0, ri0[inodekey(m)] ∈ fs0, buf-opt0.some? → # buf-opt0.buf = VFS_PAGE_SIZE, asynced0 → boolvar0 ⊦ adr1 = adr2, m = 0, orphans (abs-dirs(fs0, ri0), abs-files(fs0[adr1, truncnode(inodekey(m), min(n0, m2))][adr2, inodenode(inodekey(m), md, false, m0, 0, n0)], ri0[inodekey(m), adr2])) = abs-keys(orphans(fs0, ri0)), adr2 ∈ fs0, adr1 ∈ fs0, ∀ ino, name, n. ROOT_INO ∈ abs-dirs(fs0, ri0) ∧ ( ino ∈ abs-dirs(fs0, ri0) ∧ ino ≠ ROOT_INO ∧ links(ino, abs-dirs(fs0, ri0)) = ∅ → dir-empty(ino, abs-dirs(fs0, ri0), abs-files(fs0, ri0)[m, mkfile(n0, md, m0, abs-content(m, fs0, ri0) upto min(n0, m2))])) ∧ ( ino ∈ abs-dirs(fs0, ri0) → ¬ ino ∈ abs-files(fs0, ri0)[m, mkfile(n0, md, m0, abs-content(m, fs0, ri0) upto min(n0, m2))] ∧ abs-dirs(fs0, ri0)[ino].nlink = # links(ino, abs-dirs(fs0, ri0)) ∧ abs-dirs(fs0, ri0)[ino].nlink ≤ 1 ∧ abs-dirs(fs0, ri0)[ino].size = # abs-dirs(fs0, ri0)[ino].entries ∧ abs-dirs(fs0, ri0)[ino].nsubdirs = # subdirs(ino, abs-dirs(fs0, ri0))) ∧ ( ino ∈ abs-files(fs0, ri0)[m, mkfile(n0, md, m0, abs-content(m, fs0, ri0) upto min(n0, m2))] → ¬ ino ∈ abs-dirs(fs0, ri0) ∧ abs-files(fs0, ri0)[m, mkfile(n0, md, m0, abs-content(m, fs0, ri0) upto min(n0, m2))][ino].nlink = # links(ino, abs-dirs(fs0, ri0))) ∧ ( ino ∈ abs-dirs(fs0, ri0) ∧ name ∈ abs-dirs(fs0, ri0)[ino].entries → valid-ino (abs-dirs(fs0, ri0)[ino].entries[name], abs-dirs(fs0, ri0), abs-files(fs0, ri0)[m, mkfile(n0, md, m0, abs-content(m, fs0, ri0) upto min(n0, m2))])) ∧ ( ino ∈ abs-files(fs0, ri0)[m, mkfile(n0, md, m0, abs-content(m, fs0, ri0) upto min(n0, m2))] ∧ n ∈ abs-files(fs0, ri0)[m, mkfile(n0, md, m0, abs-content(m, fs0, ri0) upto min(n0, m2))][ino].content → valid-pagesize(ino, n, abs-files(fs0, ri0)[m, mkfile(n0, md, m0, abs-content(m, fs0, ri0) upto min(n0, m2))])) → ROOT_INO ∈ abs-dirs(fs0, ri0) ∧ ( ino ∈ abs-dirs(fs0, ri0) ∧ ino ≠ ROOT_INO ∧ links(ino, abs-dirs(fs0, ri0)) = ∅ → dir-empty (ino, abs-dirs(fs0, ri0), abs-files(fs0[adr1, truncnode(inodekey(m), min(n0, m2))][adr2, inodenode(inodekey(m), md, false, m0, 0, n0)], ri0[inodekey(m), adr2]))) ∧ ( ino ∈ abs-dirs(fs0, ri0) → ¬ ino ∈ abs-files(fs0[adr1, truncnode(inodekey(m), min(n0, m2))][adr2, inodenode(inodekey(m), md, false, m0, 0, n0)], ri0[inodekey(m), adr2]) ∧ abs-dirs(fs0, ri0)[ino].nlink = # links(ino, abs-dirs(fs0, ri0)) ∧ abs-dirs(fs0, ri0)[ino].nlink ≤ 1 ∧ abs-dirs(fs0, ri0)[ino].size = # abs-dirs(fs0, ri0)[ino].entries ∧ abs-dirs(fs0, ri0)[ino].nsubdirs = # subdirs(ino, abs-dirs(fs0, ri0))) ∧ ( ino ∈ abs-files(fs0[adr1, truncnode(inodekey(m), min(n0, m2))][adr2, inodenode(inodekey(m), md, false, m0, 0, n0)], ri0[inodekey(m), adr2]) → ¬ ino ∈ abs-dirs(fs0, ri0) ∧ abs-files(fs0[adr1, truncnode(inodekey(m), min(n0, m2))][adr2, inodenode(inodekey(m), md, false, m0, 0, n0)], ri0[inodekey(m), adr2]) [ino ] .nlink = # links(ino, abs-dirs(fs0, ri0))) ∧ ( ino ∈ abs-dirs(fs0, ri0) ∧ name ∈ abs-dirs(fs0, ri0)[ino].entries → valid-ino (abs-dirs(fs0, ri0)[ino].entries[name], abs-dirs(fs0, ri0), abs-files(fs0[adr1, truncnode(inodekey(m), min(n0, m2))][adr2, inodenode(inodekey(m), md, false, m0, 0, n0)], ri0[inodekey(m), adr2]))) ∧ ( ino ∈ abs-files(fs0[adr1, truncnode(inodekey(m), min(n0, m2))][adr2, inodenode(inodekey(m), md, false, m0, 0, n0)], ri0[inodekey(m), adr2]) ∧ n ∈ abs-files(fs0[adr1, truncnode(inodekey(m), min(n0, m2))][adr2, inodenode(inodekey(m), md, false, m0, 0, n0)], ri0[inodekey(m), adr2]) [ino ] .content → valid-pagesize (ino, n, abs-files(fs0[adr1, truncnode(inodekey(m), min(n0, m2))][adr2, inodenode(inodekey(m), md, false, m0, 0, n0)], ri0[inodekey(m), adr2]))), m2 ≤ n0 ∧ m2 % VFS_PAGE_SIZE ≠ 0 ∧ (datakey(m, m2 / VFS_PAGE_SIZE) ∈ ri0 ∨ buf-opt0.some?), m2 ≤ n0 ∧ m2 % VFS_PAGE_SIZE ≠ 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 1358:
fs0[ri0[inodekey(m)]] = inodenode(key, md0, false, m0, 0, m3), abs-files(fs0, ri0)[m, mkfile(n0, md, m0, abs-content(m, fs0, ri0) upto min(n0, m2))] = abs-files (fs0[adr1, truncnode(inodekey(m), min(n0, m2))][adr2, inodenode(inodekey(m), md, false, m0, 0, n0)], ri0[inodekey(m), adr2] \ datakeys(inodekey(m), min(n0, m2), ri0[inodekey(m), adr2])), abs-dirs(fs0, ri0) = abs-dirs(fs0[adr1, truncnode(inodekey(m), min(n0, m2))][adr2, inodenode(inodekey(m), md, false, m0, 0, n0)], ri0[inodekey(m), adr2]), fs0[ri0[inodekey(ROOT_INO)]].directory, orphans(fs0, ri0).inodes?, fo.inodes?, afs-cons(abs-dirs(fs0, ri0), abs-files(fs0, ri0)[m, mkfile(n0, md, m0, abs-content(m, fs0, ri0) upto min(n0, m2))]), afs-cons(abs-dirs(fs0, ri0), abs-files(fs0, ri0)), file-node-cons (fs0[adr1, truncnode(inodekey(m), min(n0, m2))][adr2, inodenode(inodekey(m), md, false, m0, 0, n0)], ri0[inodekey(m), adr2] \ datakeys(inodekey(m), min(n0, m2), ri0[inodekey(m), adr2])), file-node-cons(fs0, ri0), log-cons(log0, fs0), orphans-cons (fs0[adr1, truncnode(inodekey(m), min(n0, m2))][adr2, inodenode(inodekey(m), md, false, m0, 0, n0)], ri0[inodekey(m), adr2] \ datakeys(inodekey(m), min(n0, m2), ri0[inodekey(m), adr2]), orphans(fs0, ri0)), orphans-cons(fs0, ri0, orphans(fs0, ri0)), replay-cons-strong (fs0[adr1, truncnode(inodekey(m), min(n0, m2))][adr2, inodenode(inodekey(m), md, false, m0, 0, n0)], ri0[inodekey(m), adr2] \ datakeys(inodekey(m), min(n0, m2), ri0[inodekey(m), adr2]), orphans(fs0, ri0), fi, fo, (log0 + adr1 ') + adr2 '), replay-cons-strong(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ri-inj(ri0[inodekey(m), adr2] \ datakeys(inodekey(m), min(n0, m2), ri0[inodekey(m), adr2])), ri-inj(ri0), ri-inj(fi), ubifs-cons (fs0[adr1, truncnode(inodekey(m), min(n0, m2))][adr2, inodenode(inodekey(m), md, false, m0, 0, n0)], ri0[inodekey(m), adr2] \ datakeys(inodekey(m), min(n0, m2), ri0[inodekey(m), adr2]), orphans(fs0, ri0), fi, fo, (log0 + adr1 ') + adr2 '), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ri0[inodekey(m)] ∈ fs0, inodekey(m) ∈ ri0, inodekey(ROOT_INO) ∈ ri0, asynced0 → boolvar0, buf-opt0.some? → # buf-opt0.buf = VFS_PAGE_SIZE, inodekey(ino) ∈ ri0 ∧ fs0[ri0[inodekey(ino)]].directory ∧ ino ≠ ROOT_INO ∧ links(ino, abs-dirs(fs0, ri0)) = ∅ → abs-children(ino, fs0, ri0) = ∅, inodekey(ino) ∈ ri0 ∧ fs0[ri0[inodekey(ino)]].directory → fs0[ri0[inodekey(ino)]].nlink = # links(ino, abs-dirs(fs0, ri0)) ∧ fs0[ri0[inodekey(ino)]].nlink ≤ 1 ∧ fs0[ri0[inodekey(ino)]].size = # abs-children(ino, fs0, ri0) ∧ fs0[ri0[inodekey(ino)]].nsubdirs = # subdirs(ino, abs-dirs(fs0, ri0)), inodekey(ino) ∈ ri0 ∧ ¬ fs0[ri0[inodekey(ino)]].directory → (ino = m ⊃ mkfile(n0, md, m0, abs-content(m, fs0, ri0) upto min(n0, m2)) ;mkfile(fs0[ri0[inodekey(ino)]].size, fs0[ri0[inodekey(ino)]].meta, fs0[ri0[inodekey(ino)]].nlink, abs-content(ino, fs0, ri0)) ) .nlink = # links(ino, abs-dirs(fs0, ri0)), inodekey(ino) ∈ ri0 ∧ dentrykey(ino, name) ∈ ri0 → inodekey(abs-dirs(fs0, ri0)[ino].entries[name]) ∈ ri0 ∧ fs0[ri0[inodekey(abs-dirs(fs0, ri0)[ino].entries[name])]].directory ∨ inodekey(abs-dirs(fs0, ri0)[ino].entries[name]) ∈ ri0 ∧ ¬ fs0[ri0[inodekey(abs-dirs(fs0, ri0)[ino].entries[name])]].directory, inodekey(ino) ∈ ri0 ∧ ¬ fs0[ri0[inodekey(ino)]].directory ∧ n ∈ (ino = m ⊃ mkfile(n0, md, m0, abs-content(m, fs0, ri0) upto min(n0, m2)) ;mkfile(fs0[ri0[inodekey(ino)]].size, fs0[ri0[inodekey(ino)]].meta, fs0[ri0[inodekey(ino)]].nlink, abs-content(ino, fs0, ri0)) ) .content → # (ino = m ⊃ mkfile(n0, md, m0, abs-content(m, fs0, ri0) upto min(n0, m2)) ;mkfile(fs0[ri0[inodekey(ino)]].size, fs0[ri0[inodekey(ino)]].meta, fs0[ri0[inodekey(ino)]].nlink, abs-content(ino, fs0, ri0)) ) .content [n ] = VFS_PAGE_SIZE ⊦ adr1 = adr2, m = 0, orphans (abs-dirs(fs0, ri0), abs-files(fs0[adr1, truncnode(inodekey(m), min(n0, m2))][adr2, inodenode(inodekey(m), md, false, m0, 0, n0)], ri0[inodekey(m), adr2])) = abs-keys(orphans(fs0, ri0)), adr1 ∈ fs0, adr2 ∈ fs0, m2 ≤ n0 ∧ m2 % VFS_PAGE_SIZE ≠ 0, m2 ≤ n0 ∧ m2 % VFS_PAGE_SIZE ≠ 0 ∧ (datakey(m, m2 / VFS_PAGE_SIZE) ∈ ri0 ∨ buf-opt0.some?), ( inodekey(ino) ∈ ri0 ∧ fs0[ri0[inodekey(ino)]].directory → ( ¬ inodekey(ino) ∈ ri0[inodekey(m), adr2] ∨ (adr2 = (m = ino ⊃ adr2;ri0[inodekey(ino)]) ⊃ inodenode(inodekey(m), md, false, m0, 0, n0) ;(adr1 = (m = ino ⊃ adr2;ri0[inodekey(ino)]) ⊃ truncnode(inodekey(m), min(n0, m2));fs0[(m = ino ⊃ adr2;ri0[inodekey(ino)])]) ) .directory) ∧ fs0[ri0[inodekey(ino)]].nlink = # links(ino, abs-dirs(fs0, ri0)) ∧ fs0[ri0[inodekey(ino)]].nlink ≤ 1 ∧ fs0[ri0[inodekey(ino)]].size = # abs-children(ino, fs0, ri0) ∧ fs0[ri0[inodekey(ino)]].nsubdirs = # subdirs(ino, abs-dirs(fs0, ri0))) ∧ ( inodekey(ino) ∈ ri0[inodekey(m), adr2] ∧ ¬ (adr2 = (m = ino ⊃ adr2;ri0[inodekey(ino)]) ⊃ inodenode(inodekey(m), md, false, m0, 0, n0) ;(adr1 = (m = ino ⊃ adr2;ri0[inodekey(ino)]) ⊃ truncnode(inodekey(m), min(n0, m2));fs0[(m = ino ⊃ adr2;ri0[inodekey(ino)])]) ) .directory → (¬ inodekey(ino) ∈ ri0 ∨ ¬ fs0[ri0[inodekey(ino)]].directory) ∧ abs-files(fs0[adr1, truncnode(inodekey(m), min(n0, m2))][adr2, inodenode(inodekey(m), md, false, m0, 0, n0)], ri0[inodekey(m), adr2])[ino] .nlink = # 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[inodekey(m), adr2] ∧ ¬ (adr2 = (m = fs0[ri0[dentrykey(ino, name)]].ino ⊃ adr2;ri0[inodekey(fs0[ri0[dentrykey(ino, name)]].ino)]) ⊃ inodenode(inodekey(m), md, false, m0, 0, n0) ;(adr1 = (m = fs0[ri0[dentrykey(ino, name)]].ino ⊃ adr2;ri0[inodekey(fs0[ri0[dentrykey(ino, name)]].ino)]) ⊃ truncnode(inodekey(m), min(n0, m2)) ;fs0[(m = fs0[ri0[dentrykey(ino, name)]].ino ⊃ adr2;ri0[inodekey(fs0[ri0[dentrykey(ino, name)]].ino)])] ) ) .directory) ∧ ( inodekey(ino) ∈ ri0[inodekey(m), adr2] ∧ ¬ (adr2 = (m = ino ⊃ adr2;ri0[inodekey(ino)]) ⊃ inodenode(inodekey(m), md, false, m0, 0, n0) ;(adr1 = (m = ino ⊃ adr2;ri0[inodekey(ino)]) ⊃ truncnode(inodekey(m), min(n0, m2));fs0[(m = ino ⊃ adr2;ri0[inodekey(ino)])]) ) .directory ∧ n ∈ abs-files(fs0[adr1, truncnode(inodekey(m), min(n0, m2))][adr2, inodenode(inodekey(m), md, false, m0, 0, n0)], ri0[inodekey(m), adr2])[ino] .content → # abs-files(fs0[adr1, truncnode(inodekey(m), min(n0, m2))][adr2, inodenode(inodekey(m), md, false, m0, 0, n0)], ri0[inodekey(m), adr2])[ino] .content [n ] = VFS_PAGE_SIZE)

Rule argument

Additional information

Used simplifier rules: at-ri: ⊦ ri[key, adr][key0] = (key = key0 ⊃ adr;ri[key0]);%⊦ dentrykey(ino, str) ∈ ri → abs-children(ino, fs, ri)[str] = fs[ri[dentrykey(ino, str)]].ino; (s)% ⊦ fs[adr0, nd][adr1] = (adr0 = adr1 ⊃ nd;fs[adr1]); (s)% ⊦ inodekey(m) = inodekey(m0) ↔ m = m0; (s)% ⊦ afs-cons(dirs, files) → ROOT_INO ∈ dirs; (ss)%⊦ valid-pagesize(ino, n, files) ↔ # files[ino].content[n] = VFS_PAGE_SIZE; (s)% ⊦ valid-ino(ino, dirs, files) ↔ ino ∈ dirs ∨ ino ∈ files; (s)%⊦ dentrykey(ino, str) ∈ ri ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → fs[ri[inodekey(ino)]].directory; (ss)% ⊦ str ∈ abs-children(ino, fs, ri) ↔ dentrykey(ino, str) ∈ ri; (s)%⊦ 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)% ⊦ mkdir(m, md, m0, m1, entries).nsubdirs = m1; (s)% ⊦ mkdir(m, md, m0, m1, entries).size = m; (s)% ⊦ mkdir(m, md, m0, m1, entries).nlink = m0; (s)%⊦ ino ∈ abs-files(fs, ri) ↔ inodekey(ino) ∈ ri ∧ ¬ fs[ri[inodekey(ino)]].directory; (s)% ⊦ ino ∈ files[ino0, af] ↔ ino ∈ files; (s)% ⊦ mkdir(m, md, m0, m1, entries).entries = entries; (s)%⊦ abs-dir(ino, fs, ri) = mkdir (fs[ri[inodekey(ino)]].size, fs[ri[inodekey(ino)]].meta, fs[ri[inodekey(ino)]].nlink, fs[ri[inodekey(ino)]].nsubdirs, abs-children(ino, fs, ri)); (s)%⊦ inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].directory → abs-dirs(fs, ri)[ino] = abs-dir(ino, fs, ri); (s)% ⊦ dir-empty(ino, dirs, files) ↔ dirs[ino].entries = ∅; (s)%⊦ ino ∈ abs-dirs(fs, ri) ↔ inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].directory; (s)