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Proof step 49 from proof inv-truncate (previous step)

# buf-opt.buf = VFS_PAGE_SIZE, boolvar ↔ boolvar0, fs0[ri0[inodekey(m)]].nlink = 0 ∧ m ≠ ROOT_INO ↔ inodekey(m) ∈ ro, VFS_PAGE_SIZE = n0 + m3 % VFS_PAGE_SIZE, adr = adr2, fs = fs0[adr1, truncnode(inodekey(m), m3)][adr2, inodenode(inodekey(m), md0, false, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, n)] [adr3, datanode(datakey(m, m3 / VFS_PAGE_SIZE), fill(buf-opt.buf, zero, m3 % VFS_PAGE_SIZE, n0)) ], key = inodekey(m), log = ((log0 + adr1 ') + adr2 ') + adr3 ', ri = ri0[datakey(m, m3 / VFS_PAGE_SIZE), adr3], fs0[ri0[inodekey(m)]].inode?, fo.inodes?, ro.inodes?, buf-opt.some?, file-node-cons(fs0, ri0), log-cons(log0, fs0), orphans-cons(fs0, ri0, ro), replay-cons-strong(fs0, ri0, ro, fi, fo, log0), ri-inj(fi), ri-inj(ri0), ubifs-cons(fs0, ri0, ro, fi, fo, log0), inodekey(m) ∈ ri0, ri0[inodekey(m)] ∈ fs0, m3 % VFS_PAGE_SIZE + n0 ≤ # buf-opt.buf, m3 ≤ n ⊦ ⟪if ¬ adr ∈ ri ∧ adr ∈ fs ∧ key-cons(key, fs[adr]) then ri[key] := adr else abort; aubifs_core_index_truncate# (inodekey(m), m3, fi, ro, fo, fs0[adr1, truncnode(inodekey(m), m3)][adr2, inodenode(inodekey(m), md0, false, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, n)] [adr3, datanode(datakey(m, m3 / VFS_PAGE_SIZE), fill(buf-opt.buf, zero, m3 % VFS_PAGE_SIZE, n0)) ], ((log0 + adr1 ') + adr2 ') + adr3 ', boolvar0 ; ri); boolvar1 := true; inode := mkinode (m, inodenode(inodekey(m), md0, false, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, n).meta, inodenode(inodekey(m), md0, false, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, n).directory, inodenode(inodekey(m), md0, false, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, n).nlink, inodenode(inodekey(m), md0, false, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, n).nsubdirs, inodenode(inodekey(m), md0, false, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, n).size); m4 := m3; m0 := m; if boolvar1 then buf-opt0 := some (datanode(datakey(m0, m4 / VFS_PAGE_SIZE), fill(datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf-opt.buf).data, zero, m4 % VFS_PAGE_SIZE, n0)) .data)⟫ ( ubifs-cons (fs0[adr1, truncnode(inodekey(m0), m4)] [adr2, inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n) ] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), fill(buf-opt.buf, zero, m4 % VFS_PAGE_SIZE, n0)) ], ri, ro, fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 ') ∧ replay-cons-strong (fs0[adr1, truncnode(inodekey(m0), m4)] [adr2, inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n) ] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), fill(buf-opt.buf, zero, m4 % VFS_PAGE_SIZE, n0)) ], ri, ro, fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 ') ∧ file-node-cons (fs0[adr1, truncnode(inodekey(m0), m4)] [adr2, inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n) ] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), fill(buf-opt.buf, zero, m4 % VFS_PAGE_SIZE, n0)) ], ri) ∧ orphans-cons (fs0[adr1, truncnode(inodekey(m0), m4)] [adr2, inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n) ] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), fill(buf-opt.buf, zero, m4 % VFS_PAGE_SIZE, n0)) ], ri, ro)), m3 % VFS_PAGE_SIZE = 0, VFS_PAGE_SIZE = 0, adr1 = adr3, adr1 = adr2, adr2 = adr3, fs0[ri0[inodekey(m)]].directory, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0

Heuristic symbolic execution applied rule if positive right

And obtained the following new goals

Proof step 50:
# buf-opt.buf = VFS_PAGE_SIZE, fs0[ri0[inodekey(m)]].nlink = 0 ∧ m ≠ ROOT_INO ↔ inodekey(m) ∈ ro, boolvar ↔ boolvar0, VFS_PAGE_SIZE = n0 + m3 % VFS_PAGE_SIZE, adr = adr2, fs = fs0[adr1, truncnode(inodekey(m), m3)][adr2, inodenode(inodekey(m), md0, false, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, n)] [adr3, datanode(datakey(m, m3 / VFS_PAGE_SIZE), fill(buf-opt.buf, zero, m3 % VFS_PAGE_SIZE, n0)) ], key = inodekey(m), log = ((log0 + adr1 ') + adr2 ') + adr3 ', ri = ri0[datakey(m, m3 / VFS_PAGE_SIZE), adr3], fs0[ri0[inodekey(m)]].inode?, ro.inodes?, fo.inodes?, buf-opt.some?, file-node-cons(fs0, ri0), log-cons(log0, fs0), orphans-cons(fs0, ri0, ro), replay-cons-strong(fs0, ri0, ro, fi, fo, log0), ri-inj(ri0), ri-inj(fi), ubifs-cons(fs0, ri0, ro, fi, fo, log0), ri0[inodekey(m)] ∈ fs0, inodekey(m) ∈ ri0, m3 ≤ n, m3 % VFS_PAGE_SIZE + n0 ≤ # buf-opt.buf ⊦ ⟪ri[key] := adr; aubifs_core_index_truncate# (inodekey(m), m3, fi, ro, fo, fs0[adr1, truncnode(inodekey(m), m3)][adr2, inodenode(inodekey(m), md0, false, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, n)] [adr3, datanode(datakey(m, m3 / VFS_PAGE_SIZE), fill(buf-opt.buf, zero, m3 % VFS_PAGE_SIZE, n0)) ], ((log0 + adr1 ') + adr2 ') + adr3 ', boolvar0 ; ri); boolvar1 := true; inode := mkinode (m, inodenode(inodekey(m), md0, false, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, n).meta, inodenode(inodekey(m), md0, false, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, n).directory, inodenode(inodekey(m), md0, false, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, n).nlink, inodenode(inodekey(m), md0, false, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, n).nsubdirs, inodenode(inodekey(m), md0, false, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, n).size); m4 := m3; m0 := m; if boolvar1 then buf-opt0 := some (datanode(datakey(m0, m4 / VFS_PAGE_SIZE), fill(datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf-opt.buf).data, zero, m4 % VFS_PAGE_SIZE, n0)) .data)⟫ ( ubifs-cons (fs0[adr1, truncnode(inodekey(m0), m4)] [adr2, inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n) ] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), fill(buf-opt.buf, zero, m4 % VFS_PAGE_SIZE, n0)) ], ri, ro, fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 ') ∧ replay-cons-strong (fs0[adr1, truncnode(inodekey(m0), m4)] [adr2, inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n) ] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), fill(buf-opt.buf, zero, m4 % VFS_PAGE_SIZE, n0)) ], ri, ro, fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 ') ∧ file-node-cons (fs0[adr1, truncnode(inodekey(m0), m4)] [adr2, inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n) ] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), fill(buf-opt.buf, zero, m4 % VFS_PAGE_SIZE, n0)) ], ri) ∧ orphans-cons (fs0[adr1, truncnode(inodekey(m0), m4)] [adr2, inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n) ] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), fill(buf-opt.buf, zero, m4 % VFS_PAGE_SIZE, n0)) ], ri, ro)), m3 % VFS_PAGE_SIZE = 0, VFS_PAGE_SIZE = 0, adr1 = adr2, adr1 = adr3, adr2 = adr3, fs0[ri0[inodekey(m)]].directory, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0

Rule argument

pos: right 1

Additional information

Used simplifier rules: data-notin-other1: ⊦ ubifs-cons(fs, ri, ro, fi, fo, log) ∧ ¬ adr0 ∈ fs ∧ adr0 ≠ adr1 → ¬ adr0 ∈ ri[key1, adr1];%at-fs: ⊦ fs[adr0, nd][adr1] = (adr0 = adr1 ⊃ nd;fs[adr1]);% ⊦ adr ≠ adr0 → (adr ∈ fs[adr0, nd] ↔ adr ∈ fs); (s)% ⊦ adr ∈ fs[adr1, nd] ↔ adr = adr1 ∨ adr ∈ fs; (s)% ⊦ adr ≠ adr0 → fs[adr0, nd][adr] = fs[adr]; (s)%⊦ key-cons(inodekey(ino), nd) ↔ nd.inode? ∧ nd.key = inodekey(ino) ∧ ino ≠ 0; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).inode?; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).key = key; (s)% ⊦ inodekey(m) = inodekey(m0) ↔ m = m0; (s)% ⊦ ROOT_INO ≠ 0; (s)% ⊦ VFS_PAGE_SIZE ≠ 0; (s)% ⊦ ubifs-cons(fs, ri, ro, fi, fo, log) → ¬ inodekey(0) ∈ ri; (s)