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Proof step 31 from proof process-one (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 32:
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))

Rule argument

Additional information

Used simplifier rules: a: ⊦ (rx + rx0) + rx1 = rx + rx0 + rx1; from specification list[reflist]% ⊦ r ' + rx ≠ []; (s)% ⊦ r + rx = r ' + rx; (s)