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Proof step 124 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, inodekey(ino) ∈ ri0[datakey(m, m2 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2], m2 ≤ n1, asynced0 → boolvar0 ⊦ m2 % VFS_PAGE_SIZE = 0, adr1 = adr2, adr1 = adr3, adr2 = adr3, ino = m, m = 0, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, ( inodekey(ino) ∈ ri0[datakey(m, m2 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2] ∧ (adr3 = ri0[inodekey(ino)] ⊃ datanode(datakey(m, m2 / VFS_PAGE_SIZE), fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n0)) ;(adr2 = ri0[inodekey(ino)] ⊃ inodenode(inodekey(m), md, false, m0, 0, n1) ;(adr1 = ri0[inodekey(ino)] ⊃ truncnode(inodekey(m), m2);fs0[ri0[inodekey(ino)]]) ) ) .directory ↔ inodekey(ino) ∈ ri0 ∧ fs0[ri0[inodekey(ino)]].directory) ∧ ( inodekey(ino) ∈ ri0[datakey(m, m2 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2] ∧ (adr3 = ri0[inodekey(ino)] ⊃ datanode(datakey(m, m2 / VFS_PAGE_SIZE), fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n0)) ;(adr2 = ri0[inodekey(ino)] ⊃ inodenode(inodekey(m), md, false, m0, 0, n1) ;(adr1 = ri0[inodekey(ino)] ⊃ truncnode(inodekey(m), m2);fs0[ri0[inodekey(ino)]]) ) ) .directory → abs-dirs (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]) [ino ] = mkdir (fs0[ri0[inodekey(ino)]].size, fs0[ri0[inodekey(ino)]].meta, fs0[ri0[inodekey(ino)]].nlink, fs0[ri0[inodekey(ino)]].nsubdirs, abs-children(ino, fs0, ri0)))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 125:
# 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, inodekey(ino) ∈ ri0, m2 ≤ n1, asynced0 → boolvar0 ⊦ m2 % VFS_PAGE_SIZE = 0, adr1 = adr3, adr1 = adr2, adr2 = adr3, ino = m, m = 0, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, ( inodekey(ino) ∈ ri0[datakey(m, m2 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2] ∧ (adr3 = ri0[inodekey(ino)] ⊃ datanode(datakey(m, m2 / VFS_PAGE_SIZE), fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n0)) ;(adr2 = ri0[inodekey(ino)] ⊃ inodenode(inodekey(m), md, false, m0, 0, n1) ;(adr1 = ri0[inodekey(ino)] ⊃ truncnode(inodekey(m), m2);fs0[ri0[inodekey(ino)]]) ) ) .directory ↔ fs0[ri0[inodekey(ino)]].directory) ∧ ( inodekey(ino) ∈ ri0[datakey(m, m2 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2] ∧ (adr3 = ri0[inodekey(ino)] ⊃ datanode(datakey(m, m2 / VFS_PAGE_SIZE), fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n0)) ;(adr2 = ri0[inodekey(ino)] ⊃ inodenode(inodekey(m), md, false, m0, 0, n1) ;(adr1 = ri0[inodekey(ino)] ⊃ truncnode(inodekey(m), m2);fs0[ri0[inodekey(ino)]]) ) ) .directory → abs-dirs (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]) [ino ] = mkdir (fs0[ri0[inodekey(ino)]].size, fs0[ri0[inodekey(ino)]].meta, fs0[ri0[inodekey(ino)]].nlink, fs0[ri0[inodekey(ino)]].nsubdirs, abs-children(ino, fs0, ri0)))

Rule argument

Additional information

Used simplifier rules: ⊦ inodekey(m) ≠ datakey(m0, m1); (s)% ⊦ inodekey(m) = inodekey(m0) ↔ m = m0; (s)% ⊦ key ∈ ri[key0, adr] ↔ key = key0 ∨ key ∈ ri; (las)