[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 574 from proof inv-truncate (previous step)

fs0[ri[inodekey(m)]].nlink = 0 ∧ m ≠ ROOT_INO ↔ inodekey(m) ∈ ro, adr = adr2, fs = fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, fs0[ri[inodekey(m)]].nlink, fs0[ri[inodekey(m)]].nsubdirs, n)], inode = mkinode(m, md, false, fs0[ri[inodekey(m)]].nlink, fs0[ri[inodekey(m)]].nsubdirs, m2), key = inodekey(m), log = (log0 + adr1 ') + adr2 ', nd1 = inodenode(inodekey(m), md, false, fs0[ri[inodekey(m)]].nlink, fs0[ri[inodekey(m)]].nsubdirs, n), fs0[ri[inodekey(m)]].inode?, ro.inodes?, fo.inodes?, file-node-cons(fs0, ri), log-cons(log0, fs0), orphans-cons(fs0, ri, ro), replay-cons-strong(fs0, ri, ro, fi, fo, log0), ri-cons(ri, fs0), ri-inj(ri), ri-inj(fi), ubifs-cons(fs0, ri, ro, fi, fo, log0), inodekey(m) ∈ ri, ri[inodekey(m)] ∈ fs0, m2 ≤ n ⊦ ⟪if ¬ adr ∈ ri ∧ adr ∈ fs ∧ key-cons(key, fs[adr]) then ri[key] := adr else abort; aubifs_core_index_truncate#(inodekey(m), m2, fi, ro, fo, fs, (log0 + adr1 ') + adr2 ', boolvar; ri); boolvar1 := false; inode := mkinode(inode.ino, nd1.meta, nd1.directory, nd1.nlink, nd1.nsubdirs, nd1.size); if boolvar1 then buf-opt := some(nd1.data)⟫ ( ubifs-cons(fs, ri, ro, fi, fo, (log0 + adr1 ') + adr2 ') ∧ replay-cons-strong(fs, ri, ro, fi, fo, (log0 + adr1 ') + adr2 ') ∧ file-node-cons(fs, ri) ∧ orphans-cons(fs, ri, ro)), m2 % VFS_PAGE_SIZE = 0, adr1 = adr2, m = 0, fs0[ri[inodekey(m)]].directory, buf-opt.some?, adr2 ∈ fs0, adr1 ∈ fs0, datakey(m, m2 / VFS_PAGE_SIZE) ∈ ri

Heuristic symbolic execution applied rule if positive right

And obtained the following new goals

Proof step 575:
fs0[ri[inodekey(m)]].nlink = 0 ∧ m ≠ ROOT_INO ↔ inodekey(m) ∈ ro, adr = adr2, fs = fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, fs0[ri[inodekey(m)]].nlink, fs0[ri[inodekey(m)]].nsubdirs, n)], inode = mkinode(m, md, false, fs0[ri[inodekey(m)]].nlink, fs0[ri[inodekey(m)]].nsubdirs, m2), key = inodekey(m), log = (log0 + adr1 ') + adr2 ', nd1 = inodenode(inodekey(m), md, false, fs0[ri[inodekey(m)]].nlink, fs0[ri[inodekey(m)]].nsubdirs, n), fs0[ri[inodekey(m)]].inode?, fo.inodes?, ro.inodes?, file-node-cons(fs0, ri), log-cons(log0, fs0), orphans-cons(fs0, ri, ro), replay-cons-strong(fs0, ri, ro, fi, fo, log0), ri-cons(ri, fs0), ri-inj(fi), ri-inj(ri), ubifs-cons(fs0, ri, ro, fi, fo, log0), ri[inodekey(m)] ∈ fs0, inodekey(m) ∈ ri, m2 ≤ n ⊦ ⟪ri[key] := adr; aubifs_core_index_truncate#(inodekey(m), m2, fi, ro, fo, fs, (log0 + adr1 ') + adr2 ', boolvar; ri); boolvar1 := false; inode := mkinode(inode.ino, nd1.meta, nd1.directory, nd1.nlink, nd1.nsubdirs, nd1.size); if boolvar1 then buf-opt := some(nd1.data)⟫ ( ubifs-cons(fs, ri, ro, fi, fo, (log0 + adr1 ') + adr2 ') ∧ replay-cons-strong(fs, ri, ro, fi, fo, (log0 + adr1 ') + adr2 ') ∧ file-node-cons(fs, ri) ∧ orphans-cons(fs, ri, ro)), m2 % VFS_PAGE_SIZE = 0, adr1 = adr2, m = 0, fs0[ri[inodekey(m)]].directory, buf-opt.some?, datakey(m, m2 / VFS_PAGE_SIZE) ∈ ri, adr1 ∈ fs0, adr2 ∈ 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(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)% ⊦ adr ∈ ri ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → adr ∈ fs; (ss)