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Proof step 10 from proof process-one (previous step)

((del-list(to_delete0, n) * P))(H) ⊦ H[to_delete0.head].nxt = null, to_delete0 = [], (1 ≤ n → ((del-list(H[to_delete0.head].nxt ' + to_delete0.tail, n - 1) * P))(H -- to_delete0.head)) ∧ n ≠ 0

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 11:
to_delete0 = r + rx0, ((del-list(to_delete0, n) * P))(H) ⊦ H[r].nxt = null, to_delete0 = [], (1 ≤ n → ((del-list(H[r].nxt ' + rx0, n - 1) * P))(H -- r)) ∧ n ≠ 0

Rule argument

spec: list-data, inst: reflist name: elim-list-c seq: rx ≠ [] ⊦ r = rx.head ∧ rx0 = rx.tail ↔ rx = r + rx0 subst: [rx, r, rx0] → [to_delete0, r, rx]

Additional information

Used simplifier rules: rx ≠ [] ⊦ r = rx.head ∧ rx0 = rx.tail ↔ rx = r + rx0; (elim) Used terms: to_delete0, r, rx