[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 24 from proof refine-readdir (previous step)

dentries(inodekey(m), ri) ≠ dom abs-children(m, fs, ri), fs[ri[inodekey(m)]].directory, orphans(fs, ri).inodes?, fo.inodes?, afs-cons(abs-dirs(fs, ri), abs-files(fs, ri)), file-node-cons(fs, ri), log-cons(log, fs), orphans-cons(fs, ri, orphans(fs, ri)), replay-cons-strong(fs, ri, orphans(fs, ri), fi, fo, log), ri-inj(ri), ri-inj(fi), ubifs-cons(fs, ri, orphans(fs, ri), fi, fo, log), inodekey(m) ∈ ri, asynced → boolvar ⊦ ∃ strings. ⟨strings0 := strings; fail#(; ; err)⟩ ((asynced → boolvar) ∧ dentries(inodekey(m), ri) = strings0 ∧ ESUCCESS = err)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: set-basic, inst: stringset name: Extension seq: ⊦ strings = strings0 ↔ (∀ str. str ∈ strings ↔ str ∈ strings0) subst: [strings0, strings] → [dom abs-children(m, fs, ri), dentries(inodekey(m), ri)] flags: <all paths>

Additional information

Used simplifier rules: ⊦ str ∈ dentries(key, ri) ↔ dentrykey(key.ino, str) ∈ dentrykeys(key, ri); (s)% ⊦ inodekey(m).ino = m; (s)%⊦ key ∈ dentrykeys(key0, ri) ↔ key ∈ ri ∧ key.dentry? ∧ key0.inode? ∧ key.ino = key0.ino; (s)% ⊦ dentrykey(m, str).dentry?; (s)% ⊦ inodekey(m).inode?; (s)% ⊦ dentrykey(m, str).ino = m; (s)% ⊦ str ∈ dom entries ↔ str ∈ entries; (s)% ⊦ str ∈ abs-children(ino, fs, ri) ↔ dentrykey(ino, str) ∈ ri; (s) Used terms: dom abs-children(m, fs, ri), dentries(inodekey(m), ri)