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Proof step 12 from proof process-one (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 13:
H[r] = a × r0, ((del-list(r ' + rx0, n) * P))(H) ⊦ r0 = null, (1 ≤ n → ((del-list(r0 ' + rx0, n - 1) * P))(H -- r)) ∧ n ≠ 0

Rule argument

spec: cell name: elim seq: ⊦ a = ce.val ∧ r = ce.nxt ↔ ce = a × r subst: [ce, a, r] → [H[r], a, r0]

Additional information

Used simplifier rules: ⊦ a = ce.val ∧ r = ce.nxt ↔ ce = a × r; (elim) Used terms: H[r], a, r0