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Proof step 1011 from proof refine-truncate (previous step)

fs0[ri0[inodekey(m)]] = inodenode(key0, md0, false, m1, 0, m4), orphans(fs0, ri0).inodes?, fo.inodes?, afs-cons(abs-dirs(fs0, ri0), abs-files(fs0, ri0)[m, mkfile(n0, md, m1, abs-content(m, fs0, ri0) 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, m1, 0, n0)], ri0[inodekey(m), adr2] \ datakeys(inodekey(m), m2, ri0[inodekey(m), adr2])), file-node-cons(fs0, ri0), log-cons(log0, fs0), orphans-cons (fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, m1, 0, n0)], ri0[inodekey(m), adr2] \ datakeys(inodekey(m), m2, ri0[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, m1, 0, n0)], ri0[inodekey(m), adr2] \ datakeys(inodekey(m), 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), m2, ri0[inodekey(m), adr2])), ri-inj(ri0), ri-inj(fi), ubifs-cons (fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, m1, 0, n0)], ri0[inodekey(m), adr2] \ datakeys(inodekey(m), m2, ri0[inodekey(m), adr2]), orphans(fs0, ri0), fi, fo, (log0 + adr1 ') + adr2 '), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), datakey(ino, n) ∈ ri0, inodekey(m) ∈ ri0, ri0[inodekey(m)] ∈ fs0, inodekey(ino) ∈ ri0, datakey(ino, n) ∈ ri0[inodekey(m), adr2] \ datakeys(inodekey(m), m2, ri0[inodekey(m), adr2]), m2 ≤ n0, asynced0 → boolvar0 ⊦ m2 % VFS_PAGE_SIZE = 0, fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, m1, 0, n0)] [(ri0[inodekey(m), adr2] \ datakeys(inodekey(m), m2, ri0[inodekey(m), adr2]))[datakey(ino, n)] ] .data = fs0[ri0[datakey(ino, n)]].data, adr1 = adr2, adr1 = ri0[inodekey(ino)], adr2 = ri0[inodekey(ino)], ino = m, m = 0, fs0[ri0[inodekey(ino)]].directory, buf-opt0.some?, datakey(m, m2 / VFS_PAGE_SIZE) ∈ ri0, adr1 ∈ fs0, adr2 ∈ fs0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 1012:
fs0[ri0[inodekey(m)]] = inodenode(key0, md0, false, m1, 0, m4), 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, m1, abs-content(m, fs0, ri0) upto m2)]), file-node-cons(fs0, ri0), file-node-cons (fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, m1, 0, n0)], ri0[inodekey(m), adr2] \ datakeys(inodekey(m), m2, ri0[inodekey(m), adr2])), log-cons(log0, fs0), orphans-cons(fs0, ri0, orphans(fs0, ri0)), orphans-cons (fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, m1, 0, n0)], ri0[inodekey(m), adr2] \ datakeys(inodekey(m), 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), m2)][adr2, inodenode(inodekey(m), md, false, m1, 0, n0)], ri0[inodekey(m), adr2] \ datakeys(inodekey(m), 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), m2, ri0[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, m1, 0, n0)], ri0[inodekey(m), adr2] \ datakeys(inodekey(m), m2, ri0[inodekey(m), adr2]), orphans(fs0, ri0), fi, fo, (log0 + adr1 ') + adr2 '), inodekey(ino) ∈ ri0, ri0[inodekey(m)] ∈ fs0, inodekey(m) ∈ ri0, datakey(ino, n) ∈ ri0, m2 ≤ n0, asynced0 → boolvar0 ⊦ m2 % VFS_PAGE_SIZE = 0, (adr2 = ri0[datakey(ino, n)] ⊃ inodenode(inodekey(m), md, false, m1, 0, n0) ;(adr1 = ri0[datakey(ino, n)] ⊃ truncnode(inodekey(m), m2);fs0[ri0[datakey(ino, n)]]) ) .data = fs0[ri0[datakey(ino, n)]].data, adr1 = ri0[inodekey(ino)], adr1 = adr2, adr2 = ri0[inodekey(ino)], ino = m, m = 0, fs0[ri0[inodekey(ino)]].directory, buf-opt0.some?, adr2 ∈ fs0, adr1 ∈ fs0, datakey(m, m2 / VFS_PAGE_SIZE) ∈ ri0

Rule argument

Additional information

Used simplifier rules: at-ri: ⊦ ri[key, adr][key0] = (key = key0 ⊃ adr;ri[key0]);% ⊦ key ∈ ri[key0, adr] ↔ key = key0 ∨ key ∈ ri; (las)% ⊦ key ∈ ri \ ks ↔ key ∈ ri ∧ ¬ key ∈ ks; (ls)% ⊦ fs[adr0, nd][adr1] = (adr0 = adr1 ⊃ nd;fs[adr1]); (s)% ⊦ inodekey(m) ≠ datakey(m0, m1); (s)% ⊦ inodekey(m).ino = m; (s)% ⊦ datakey(m, m0).ino = m; (s)% ⊦ inodekey(m).inode?; (s)% ⊦ datakey(m, m0).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)% ⊦ (ri \ ks)[key] = (key ∈ ks ⊃ (∅)[key];ri[key]); (s)