[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 2 from proof refine-iget (previous step)

dirs = abs-dirs(fs, ri), err = err0, files = abs-files(fs, ri), inode = p_inode, orphans(dirs, files) = abs-keys(ro), fo.inodes?, ro.inodes?, afs-cons(dirs, files), file-node-cons(fs, ri), log-cons(log, fs), orphans-cons(fs, ri, ro), pre-iget(ino, dirs, files), replay-cons-strong(fs, ri, ro, fi, fo, log), ri-inj(fi), ri-inj(ri), ubifs-cons(fs, ri, ro, fi, fo, log), asynced → boolvar ⊦ ⟪aubifs_iget#(ino, ri, fi, ro, fo, fs, log, boolvar; inode, err)⟫ ⟨afs_iget#(ino, dirs, files, asynced; p_inode, err0)⟩ ( (dirs = abs-dirs(fs, ri) ∧ files = abs-files(fs, ri) ∧ orphans(dirs, files) = abs-keys(ro) ∧ (asynced → boolvar)) ∧ inode = p_inode ∧ err = err0)

User applied rule insert program lemma

And obtained the following new goals

Proof step 3:
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), ri-inj(ri), ri-inj(fi), log-cons(log, fs), ro.inodes?, fo.inodes?, pre-iget(ino, fs, ri) ⊦ ⟪aubifs_iget#(ino, ri, fi, ro, fo, fs, log, boolvar; inode, err)⟫ true
Proof step 4:
boolvar0 ↔ boolvar, dirs = abs-dirs(fs, ri), err = err0, fi0 = fi, files = abs-files(fs, ri), fo0 = fo, fs0 = fs, ino0 = ino, inode = p_inode, log0 = log, orphans(dirs, files) = abs-keys(ro), ri0 = ri, ro0 = ro, ro.inodes?, fo.inodes?, afs-cons(dirs, files), file-node-cons(fs, ri), log-cons(log, fs), orphans-cons(fs, ri, ro), pre-iget(ino, dirs, files), pre-iget(ino, fs, ri), replay-cons-strong(fs, ri, ro, fi, fo, log), ri-inj(ri), ri-inj(fi), ubifs-cons(fs, ri, ro, fi, fo, log), asynced → boolvar ⊦ [aubifs_iget#(ino, ri, fi, ro, fo, fs, log, boolvar; inode, err)] ( true → ⟨afs_iget#(ino, dirs, files, asynced; p_inode, err0)⟩ ( (dirs = abs-dirs(fs, ri) ∧ files = abs-files(fs, ri) ∧ orphans(dirs, files) = abs-keys(ro) ∧ (asynced → boolvar)) ∧ inode = p_inode ∧ err = err0))

Rule argument

spec: aubifs-asm name: inv-iget seq: 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), ri-inj(ri), ri-inj(fi), log-cons(log, fs), ro.inodes?, fo.inodes?, pre-iget(ino, fs, ri) ⊦ ⟪aubifs_iget# (ino, ri, fi, ro, fo, fs, log, boolvar; inode, err)⟫ true subst: [boolvar, log, fs, fo, ro, fi, ri, ino, err, inode] → [boolvar, log, fs, fo, ro, fi, ri, ino, err, inode] flags: <all paths>

Additional information

Used simplifier rules: ⊦ afs-cons(abs-dirs(fs, ri), abs-files(fs, ri)) → orphans(abs-dirs(fs, ri), abs-files(fs, ri)) = abs-keys(orphans(fs, ri)); (s)%⊦ ro.inodes? → (abs-keys(ro) = abs-keys(orphans(fs, ri)) ↔ ro = orphans(fs, ri)); (s)% ⊦ pre-iget(ino, dirs, files) ↔ valid-ino(ino, dirs, files); (s)% ⊦ valid-ino(ino, dirs, files) ↔ ino ∈ dirs ∨ ino ∈ files; (s)%⊦ ino ∈ abs-dirs(fs, ri) ↔ inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].directory; (s)%⊦ ino ∈ abs-files(fs, ri) ↔ inodekey(ino) ∈ ri ∧ ¬ fs[ri[inodekey(ino)]].directory; (s)% ⊦ ubifs-cons(fs, ri, ro, fi, fo, log) → 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)% ⊦ pre-iget(ino, fs, ri) ↔ valid-ino(ino, fs, ri); (s)% ⊦ valid-ino(ino, fs, ri) ↔ inodekey(ino) ∈ ri; (s)