[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 rename-root (previous step)

root0[parent(path')].dir?, root0.dir?, py(user, parent(path'), root0, fs), py(user, parent(path), root0, fs), parent(path') ∈ root0, path ∈ root0, path ⊑ parent(path'), root0[path].dir? → pw(user, path, root0, fs), path' ∈ root0 ∧ root0[path'].dir? → root0[path'].entries = ∅, path' ∈ root0 → (root0[path].dir? ↔ root0[path'].dir?) ⊦ path' = ε, (root0 -- path)[path', root0[path]].dir?, path ⊑ path', path' ∈ root0 ∧ ¬ root0[path'].dir? ∧ ¬ root0[path'].fid ∈ ofh.fids ∧ ¬ root0[path'].fid ∈ (root0 -- path)[path', root0[path]].fids

User applied rule insert elim lemma

And closed the goal!

Rule argument

spec: path name: parent-elim seq: p ≠ ε ⊦ q = parent(p) ∧ str = p.last ↔ p = q + str ' subst: [p, q, str] → [path', q, str]

Additional information

Used simplifier rules: ⊦ p + str ' ≠ ε; (s)%a: ⊦ (p + p0) + p1 = p + p0 + p1; from specification list[path]% ⊦ ¬ p ⊑ p0 + p1 → ¬ p ⊑ p0; (s)%p ≠ ε ⊦ q = parent(p) ∧ str = p.last ↔ p = q + str '; (elim) Used terms: path', q, str