[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 256 from proof inv-truncate (previous step)

fs[ri[inodekey(m)]].nlink = 0 ∧ m ≠ ROOT_INO ↔ inodekey(m) ∈ ro, m2 % VFS_PAGE_SIZE ≠ 0, fs[ri[inodekey(m)]].inode?, ro.inodes?, fo.inodes?, file-node-cons(fs, ri), log-cons(log, fs), orphans-cons(fs, ri, ro), replay-cons-strong(fs, ri, ro, fi, fo, log), ri-inj(ri), ri-inj(fi), ubifs-cons(fs, ri, ro, fi, fo, log), ri[inodekey(m)] ∈ fs, inodekey(m) ∈ ri, m2 ≤ n, ¬ fs[ri[inodekey(m)]].directory, ¬ buf-opt.some? ⊦ ⟪aubifs_core_index_lookup#(datakey(m, m2 / VFS_PAGE_SIZE), ri, fi, ro, fo, fs, log, boolvar0; boolvar, nd; err); pageno := min(n, mkinode(m, md, false, fs[ri[inodekey(m)]].nlink, fs[ri[inodekey(m)]].nsubdirs, m2).size); key1 := inodekey(mkinode(m, md, false, fs[ri[inodekey(m)]].nlink, fs[ri[inodekey(m)]].nsubdirs, m2).ino); key0 := inodekey(mkinode(m, md, false, fs[ri[inodekey(m)]].nlink, fs[ri[inodekey(m)]].nsubdirs, m2).ino); nd0 := inodenode(inodekey(m), md, false, fs[ri[inodekey(m)]].nlink, fs[ri[inodekey(m)]].nsubdirs, n); inode := mkinode(m, md, false, fs[ri[inodekey(m)]].nlink, fs[ri[inodekey(m)]].nsubdirs, m2); if err = ESUCCESS then if boolvar then {nd.data := fill (nd.data, zero, mkinode(m, md, false, fs[ri[inodekey(m)]].nlink, fs[ri[inodekey(m)]].nsubdirs, m2).size % VFS_PAGE_SIZE, VFS_PAGE_SIZE - mkinode(m, md, false, fs[ri[inodekey(m)]].nlink, fs[ri[inodekey(m)]].nsubdirs, m2).size % VFS_PAGE_SIZE); aubifs_core_journal_add3#(truncnode(inodekey(m), min(n, m2)), nd0, nd, ri, fi, ro, fo; adr1, adr0, adr, fs, log; boolvar0, err); if err = ESUCCESS then aubifs_core_index_store#(datakey(m, m2 / VFS_PAGE_SIZE), adr, fi, ro, fo, fs, log, boolvar0; ri)} else aubifs_core_journal_add2#(truncnode(inodekey(m), min(n, m2)), nd0, ri, fi, ro, fo; adr1, adr0, fs, log; boolvar0, err); if err = ESUCCESS then {aubifs_core_index_store#(key0, adr0, fi, ro, fo, fs, log, boolvar0; ri); aubifs_core_index_truncate#(key1, pageno, fi, ro, fo, fs, log, boolvar0; ri); boolvar1 := boolvar; inode := mkinode(inode.ino, nd0.meta, nd0.directory, nd0.nlink, nd0.nsubdirs, nd0.size); if boolvar1 then buf-opt := some(nd.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))

User applied rule insert program lemma

And obtained the following new goals

Proof step 257:
ri-inj(ri), ri-inj(fi), log-cons(log, fs), ro.inodes?, fo.inodes?, ri-cons(ri, fs) ⊦ ⟪aubifs_core_index_lookup#(key, ri, fi, ro, fo, fs, log, boolvar; boolvar0, nd; err)⟫ true
Proof step 258:
fs[ri[inodekey(m)]].nlink = 0 ∧ m ≠ ROOT_INO ↔ inodekey(m) ∈ ro, boolvar2 ↔ boolvar0, fi0 = fi, fo0 = fo, fs0 = fs, key2 = datakey(m, m2 / VFS_PAGE_SIZE), log0 = log, ri0 = ri, ro0 = ro, fs[ri[inodekey(m)]].inode?, ro.inodes?, fo.inodes?, file-node-cons(fs, ri), log-cons(log, fs), orphans-cons(fs, ri, ro), replay-cons-strong(fs, ri, ro, fi, fo, log), ri-cons(ri, fs), ri-inj(ri), ri-inj(fi), ubifs-cons(fs, ri, ro, fi, fo, log), inodekey(m) ∈ ri, ri[inodekey(m)] ∈ fs, m2 ≤ n ⊦ [aubifs_core_index_lookup#(datakey(m, m2 / VFS_PAGE_SIZE), ri, fi, ro, fo, fs, log, boolvar0; boolvar, nd; err)] ( true → ⟪pageno := min(n, mkinode(m, md, false, fs[ri[inodekey(m)]].nlink, fs[ri[inodekey(m)]].nsubdirs, m2).size); key1 := inodekey(mkinode(m, md, false, fs[ri[inodekey(m)]].nlink, fs[ri[inodekey(m)]].nsubdirs, m2).ino); key0 := inodekey(mkinode(m, md, false, fs[ri[inodekey(m)]].nlink, fs[ri[inodekey(m)]].nsubdirs, m2).ino); nd0 := inodenode(inodekey(m), md, false, fs[ri[inodekey(m)]].nlink, fs[ri[inodekey(m)]].nsubdirs, n); inode := mkinode(m, md, false, fs[ri[inodekey(m)]].nlink, fs[ri[inodekey(m)]].nsubdirs, m2); if err = ESUCCESS then if boolvar then {nd.data := fill (nd.data, zero, mkinode(m, md, false, fs[ri[inodekey(m)]].nlink, fs[ri[inodekey(m)]].nsubdirs, m2).size % VFS_PAGE_SIZE, VFS_PAGE_SIZE - mkinode(m, md, false, fs[ri[inodekey(m)]].nlink, fs[ri[inodekey(m)]].nsubdirs, m2).size % VFS_PAGE_SIZE); aubifs_core_journal_add3# (truncnode(inodekey(m), min(n, m2)), nd0, nd, ri, fi, ro, fo; adr1, adr0, adr, fs, log; boolvar0, err); if err = ESUCCESS then aubifs_core_index_store#(datakey(m, m2 / VFS_PAGE_SIZE), adr, fi, ro, fo, fs, log, boolvar0; ri)} else aubifs_core_journal_add2#(truncnode(inodekey(m), min(n, m2)), nd0, ri, fi, ro, fo; adr1, adr0, fs, log; boolvar0, err); if err = ESUCCESS then {aubifs_core_index_store#(key0, adr0, fi, ro, fo, fs, log, boolvar0; ri); aubifs_core_index_truncate#(key1, pageno, fi, ro, fo, fs, log, boolvar0; ri); boolvar1 := boolvar; inode := mkinode(inode.ino, nd0.meta, nd0.directory, nd0.nlink, nd0.nsubdirs, nd0.size); if boolvar1 then buf-opt := some(nd.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))), m2 % VFS_PAGE_SIZE = 0, fs[ri[inodekey(m)]].directory, buf-opt.some?

Rule argument

spec: aubifs-internal-asm name: inv-lookup seq: ri-inj(ri), ri-inj(fi), log-cons(log, fs), ro.inodes?, fo.inodes?, ri-cons(ri, fs) ⊦ ⟪aubifs_core_index_lookup# (key, ri, fi, ro, fo, fs, log, boolvar; boolvar0, nd; err)⟫ true subst: [boolvar, log, fs, fo, ro, fi, ri, key, nd, boolvar0, err] → [boolvar0, log, fs, fo, ro, fi, ri, datakey(m, m2 / VFS_PAGE_SIZE), nd, boolvar, err] flags: <all paths>

Additional information

Used simplifier rules: ⊦ ri-cons(ri, fs) → ri-inj(ri); (ss)% ⊦ ubifs-cons(fs, ri, ro, fi, fo, log) → log-cons(log, fs); (ss)% ⊦ ubifs-cons(fs, ri, ro, fi, fo, log) → ro.inodes?; (ss)% ⊦ ubifs-cons(fs, ri, ro, fi, fo, log) → fo.inodes?; (ss)% ⊦ ubifs-cons(fs, ri, ro, fi, fo, log) → ri-cons(ri, fs); (ss)