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Proof step 4 from proof px-to-parent (previous step)

px(user, p, st) ⊦ p = ε, px(user, parent(p), st)

User applied rule insert elim lemma

And obtained the following new goals

Proof step 5:
⊦ px(user, p + q, st) → px(user, p, st)

Rule argument

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

Additional information

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