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Proof step 32 from proof process-one (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 33:
H[r] = a × r0, r0 = null, ((del-list(r ' + rx0, n) * P))(H) ⊦ (1 ≤ n → ((del-list(rx0, n - 1) * P))(H -- r)) ∧ (n = 0 → rx0 = [] ∧ P(H -- r))

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