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Proof step 1358 from proof refine-truncate (previous step)

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)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 1359:
(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, m4, content), 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]), fs0[ri0[inodekey(ROOT_INO)]].directory, 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(ROOT_INO) ∈ ri0, inodekey(m) ∈ ri0, ri0[inodekey(m)] ∈ fs0, inodekey(ino) ∈ ri0 ∧ ¬ fs0[ri0[inodekey(ino)]].directory ∧ n ∈ content → # content[n] = VFS_PAGE_SIZE, 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 → m4 = # links(ino, abs-dirs(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 ≠ ROOT_INO ∧ links(ino, abs-dirs(fs0, ri0)) = ∅ → abs-children(ino, fs0, ri0) = ∅, 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, ( 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), m2 ≤ n0 ∧ m2 % VFS_PAGE_SIZE ≠ 0 ∧ (datakey(m, m2 / VFS_PAGE_SIZE) ∈ ri0 ∨ buf-opt0.some?), m2 ≤ n0 ∧ m2 % VFS_PAGE_SIZE ≠ 0

Rule argument

spec: abstract-file name: elim seq: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content) subst: [af, m, md, m0, 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)) ), m1, md1, m4, content]

Additional information

Used simplifier rules: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content); (elim) Used terms: (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)) ), m1, md1, m4, content