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Proof step 42 from proof inv-truncate (previous step)

# buf-opt.buf = VFS_PAGE_SIZE, boolvar ↔ boolvar0, fs0[ri[inodekey(m0)]].nlink = 0 ∧ m0 ≠ ROOT_INO ↔ inodekey(m0) ∈ ro, VFS_PAGE_SIZE = n0 + m4 % VFS_PAGE_SIZE, adr = adr3, fs = fs0[adr1, truncnode(inodekey(m0), m4)][adr2, inodenode(inodekey(m0), md, false, fs0[ri[inodekey(m0)]].nlink, fs0[ri[inodekey(m0)]].nsubdirs, n)] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), fill(buf-opt.buf, zero, m4 % VFS_PAGE_SIZE, n0)) ], inode = mkinode(m0, md, false, fs0[ri[inodekey(m0)]].nlink, fs0[ri[inodekey(m0)]].nsubdirs, m4), key = datakey(m0, m4 / VFS_PAGE_SIZE), log = ((log0 + adr1 ') + adr2 ') + adr3 ', nd0 = inodenode(inodekey(m0), md, false, fs0[ri[inodekey(m0)]].nlink, fs0[ri[inodekey(m0)]].nsubdirs, n), fs0[ri[inodekey(m0)]].inode?, fo.inodes?, ro.inodes?, buf-opt.some?, file-node-cons(fs0, ri), log-cons(log0, fs0), orphans-cons(fs0, ri, ro), replay-cons-strong(fs0, ri, ro, fi, fo, log0), ri-inj(fi), ri-inj(ri), ubifs-cons(fs0, ri, ro, fi, fo, log0), inodekey(m0) ∈ ri, ri[inodekey(m0)] ∈ fs0, m4 ≤ n ⊦ ⟪if ¬ adr ∈ ri ∧ adr ∈ fs ∧ key-cons(key, fs[adr]) then ri[key] := adr else abort; log := ((log0 + adr1 ') + adr2 ') + adr3 '; aubifs_core_index_store#(inodekey(m0), adr2, fi, ro, fo, fs, log, boolvar0; ri); aubifs_core_index_truncate#(inodekey(m0), m4, fi, ro, fo, fs, log, boolvar0; ri); boolvar1 := true; inode := mkinode(inode.ino, nd0.meta, nd0.directory, nd0.nlink, nd0.nsubdirs, nd0.size); 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(fs, ri, ro, fi, fo, log) ∧ replay-cons-strong(fs, ri, ro, fi, fo, log) ∧ file-node-cons(fs, ri) ∧ orphans-cons(fs, ri, ro)), m4 % VFS_PAGE_SIZE = 0, VFS_PAGE_SIZE = 0, adr1 = adr3, adr1 = adr2, adr2 = adr3, fs0[ri[inodekey(m0)]].directory, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0

Heuristic symbolic execution applied rule if positive right

And obtained the following new goals

Proof step 43:
# buf-opt.buf = VFS_PAGE_SIZE, fs0[ri[inodekey(m0)]].nlink = 0 ∧ m0 ≠ ROOT_INO ↔ inodekey(m0) ∈ ro, boolvar ↔ boolvar0, VFS_PAGE_SIZE = n0 + m4 % VFS_PAGE_SIZE, adr = adr3, fs = fs0[adr1, truncnode(inodekey(m0), m4)][adr2, inodenode(inodekey(m0), md, false, fs0[ri[inodekey(m0)]].nlink, fs0[ri[inodekey(m0)]].nsubdirs, n)] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), fill(buf-opt.buf, zero, m4 % VFS_PAGE_SIZE, n0)) ], inode = mkinode(m0, md, false, fs0[ri[inodekey(m0)]].nlink, fs0[ri[inodekey(m0)]].nsubdirs, m4), key = datakey(m0, m4 / VFS_PAGE_SIZE), log = ((log0 + adr1 ') + adr2 ') + adr3 ', nd0 = inodenode(inodekey(m0), md, false, fs0[ri[inodekey(m0)]].nlink, fs0[ri[inodekey(m0)]].nsubdirs, n), fs0[ri[inodekey(m0)]].inode?, ro.inodes?, fo.inodes?, buf-opt.some?, file-node-cons(fs0, ri), log-cons(log0, fs0), orphans-cons(fs0, ri, ro), replay-cons-strong(fs0, ri, ro, fi, fo, log0), ri-inj(ri), ri-inj(fi), ubifs-cons(fs0, ri, ro, fi, fo, log0), ri[inodekey(m0)] ∈ fs0, inodekey(m0) ∈ ri, m4 ≤ n ⊦ ⟪ri[key] := adr; log := ((log0 + adr1 ') + adr2 ') + adr3 '; aubifs_core_index_store#(inodekey(m0), adr2, fi, ro, fo, fs, log, boolvar0; ri); aubifs_core_index_truncate#(inodekey(m0), m4, fi, ro, fo, fs, log, boolvar0; ri); boolvar1 := true; inode := mkinode(inode.ino, nd0.meta, nd0.directory, nd0.nlink, nd0.nsubdirs, nd0.size); 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(fs, ri, ro, fi, fo, log) ∧ replay-cons-strong(fs, ri, ro, fi, fo, log) ∧ file-node-cons(fs, ri) ∧ orphans-cons(fs, ri, ro)), m4 % VFS_PAGE_SIZE = 0, VFS_PAGE_SIZE = 0, adr1 = adr2, adr1 = adr3, adr2 = adr3, fs0[ri[inodekey(m0)]].directory, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0

Rule argument

pos: right 1

Additional information

Used simplifier rules: at-fs: ⊦ fs[adr0, nd][adr1] = (adr0 = adr1 ⊃ nd;fs[adr1]);% ⊦ adr ∈ fs[adr1, nd] ↔ adr = adr1 ∨ adr ∈ fs; (s)% ⊦ key-cons(datakey(ino, n), nd) ↔ nd.data? ∧ nd.key = datakey(ino, n); (s)% ⊦ datanode(key, buf).data?; (s)% ⊦ datanode(key, buf).key = key; (s)% ⊦ VFS_PAGE_SIZE ≠ 0; (s)% ⊦ adr ∈ ri ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → adr ∈ fs; (ss)