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Proof step 14 from proof px-last (previous step)

px(user, meta(p, ino, dirs, files)), q ⊑ p, ∀ q. q ⊑ parent(p) → px(user, meta(q, ino, dirs, files)) ⊦ px(user, meta(q, ino, dirs, files)), q ⊑ parent(p)

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] → [p, q0, str]

Additional information

Used simplifier rules: ⊦ p + str ' ≠ ε; (s)%a: ⊦ (p + p0) + p1 = p + p0 + p1; from specification list[path]% ⊦ ¬ p ⊑ p0 → (p ⊑ p0 + str ' ↔ p0 + str ' = p); (s)% ⊦ p ⊑ ε ↔ p = ε; (s)%p ≠ ε ⊦ q = parent(p) ∧ str = p.last ↔ p = q + str '; (elim) Used terms: p, q0, str