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Proof step 1374 from proof refine-truncate (previous step)

(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)) ) = mkfile(m1, md1, # links(ino, abs-dirs(fs0, ri0)), content), abs-dirs(fs0, ri0)[ino] = mkdir(m7, md3, m8, m9, entries), 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]), inodekey(ino) = inodekey(m), 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), inodekey(ino) ∈ ri0, ri0[inodekey(m)] ∈ fs0, inodekey(m) ∈ ri0, inodekey(ROOT_INO) ∈ ri0, asynced0 → boolvar0, buf-opt0.some? → # buf-opt0.buf = VFS_PAGE_SIZE, n ∈ content → # 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)), (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)]].directory, adr1 ∈ fs0, adr2 ∈ fs0, dentrykey(ino, name) ∈ 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)])]) ) .nlink = # links(ino, abs-dirs(fs0, ri0))) ∧ ( inodekey(ino) ∈ ri0[inodekey(m), adr2] ∧ datakey(ino, n) ∈ ri0[inodekey(m), adr2] → # (adr2 = ri0[datakey(ino, n)] ⊃ inodenode(inodekey(m), md, false, m0, 0, n0) ;(adr1 = ri0[datakey(ino, n)] ⊃ truncnode(inodekey(m), min(n0, m2));fs0[ri0[datakey(ino, n)]]) ) .data = VFS_PAGE_SIZE), m2 ≤ n0 ∧ m2 % VFS_PAGE_SIZE ≠ 0, m2 ≤ n0 ∧ m2 % VFS_PAGE_SIZE ≠ 0 ∧ (datakey(m, m2 / VFS_PAGE_SIZE) ∈ ri0 ∨ buf-opt0.some?)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 1375:
abs-dirs(fs0, ri0)[m] = mkdir(m7, md3, m8, m9, entries), fs0[ri0[inodekey(m)]] = inodenode(key, md0, false, # links(m, abs-dirs(fs0, ri0)), 0, m3), abs-files(fs0, ri0)[m, mkfile(m1, md, # links(m, abs-dirs(fs0, ri0)), abs-content(m, fs0, ri0) upto min(m1, m2))] = abs-files (fs0[adr1, truncnode(inodekey(m), min(m1, m2))][adr2, inodenode(inodekey(m), md, false, # links(m, abs-dirs(fs0, ri0)), 0, m1)], ri0[inodekey(m), adr2] \ datakeys(inodekey(m), min(m1, m2), ri0[inodekey(m), adr2])), abs-dirs(fs0, ri0) = abs-dirs (fs0[adr1, truncnode(inodekey(m), min(m1, m2))][adr2, inodenode(inodekey(m), md, false, # links(m, abs-dirs(fs0, ri0)), 0, m1)], 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(m1, md, # links(m, abs-dirs(fs0, ri0)), abs-content(m, fs0, ri0) upto min(m1, m2))]), afs-cons(abs-dirs(fs0, ri0), abs-files(fs0, ri0)), file-node-cons (fs0[adr1, truncnode(inodekey(m), min(m1, m2))][adr2, inodenode(inodekey(m), md, false, # links(m, abs-dirs(fs0, ri0)), 0, m1)], ri0[inodekey(m), adr2] \ datakeys(inodekey(m), min(m1, m2), ri0[inodekey(m), adr2])), file-node-cons(fs0, ri0), log-cons(log0, fs0), orphans-cons (fs0[adr1, truncnode(inodekey(m), min(m1, m2))][adr2, inodenode(inodekey(m), md, false, # links(m, abs-dirs(fs0, ri0)), 0, m1)], ri0[inodekey(m), adr2] \ datakeys(inodekey(m), min(m1, m2), ri0[inodekey(m), adr2]), orphans(fs0, ri0)), orphans-cons(fs0, ri0, orphans(fs0, ri0)), replay-cons-strong (fs0[adr1, truncnode(inodekey(m), min(m1, m2))][adr2, inodenode(inodekey(m), md, false, # links(m, abs-dirs(fs0, ri0)), 0, m1)], ri0[inodekey(m), adr2] \ datakeys(inodekey(m), min(m1, 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(m1, m2), ri0[inodekey(m), adr2])), ri-inj(ri0), ri-inj(fi), ubifs-cons (fs0[adr1, truncnode(inodekey(m), min(m1, m2))][adr2, inodenode(inodekey(m), md, false, # links(m, abs-dirs(fs0, ri0)), 0, m1)], ri0[inodekey(m), adr2] \ datakeys(inodekey(m), min(m1, m2), ri0[inodekey(m), adr2]), orphans(fs0, ri0), fi, fo, (log0 + adr1 ') + adr2 '), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), datakey(m, n) ∈ ri0, ri0[inodekey(m)] ∈ fs0, inodekey(ROOT_INO) ∈ ri0, inodekey(m) ∈ ri0, asynced0 → boolvar0, buf-opt0.some? → # buf-opt0.buf = VFS_PAGE_SIZE, n * VFS_PAGE_SIZE < min(m1, m2) → # (abs-content(m, fs0, ri0) upto min(m1, m2))[n] = VFS_PAGE_SIZE ⊦ # (adr2 = ri0[datakey(m, n)] ⊃ inodenode(inodekey(m), md, false, # links(m, abs-dirs(fs0, ri0)), 0, m1) ;(adr1 = ri0[datakey(m, n)] ⊃ truncnode(inodekey(m), min(m1, m2));fs0[ri0[datakey(m, n)]]) ) .data = VFS_PAGE_SIZE, adr1 = adr2, m = 0, orphans (abs-dirs(fs0, ri0), abs-files (fs0[adr1, truncnode(inodekey(m), min(m1, m2))][adr2, inodenode(inodekey(m), md, false, # links(m, abs-dirs(fs0, ri0)), 0, m1)], ri0[inodekey(m), adr2])) = abs-keys(orphans(fs0, ri0)), adr1 ∈ fs0, adr2 ∈ fs0, dentrykey(m, name) ∈ ri0, m2 ≤ m1 ∧ m2 % VFS_PAGE_SIZE ≠ 0, m2 ≤ m1 ∧ m2 % VFS_PAGE_SIZE ≠ 0 ∧ (datakey(m, m2 / VFS_PAGE_SIZE) ∈ ri0 ∨ buf-opt0.some?)

Rule argument

Additional information

Used simplifier rules: ⊦ n ∈ abs-content(ino, fs, ri) ↔ datakey(ino, n) ∈ ri; (s)% ⊦ m ∈ content upto n ↔ m * VFS_PAGE_SIZE < n ∧ m ∈ content; (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% ⊦ inodekey(m) ≠ datakey(m0, m1); (s)% ⊦ key ∈ ri[key0, adr] ↔ key = key0 ∨ key ∈ ri; (las)% ⊦ inodenode(key, md, boolvar, m, m0, m1).nlink = m; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).directory ↔ boolvar; (s)%⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0; (ws)% ⊦ inodekey(m) = inodekey(m0) ↔ m = m0; (s)