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Proof step 13 from proof process-queue (previous step)

n ≠ 0, ((del-list(to_delete, n) * P))(H), ((del-list(to_delete0, n - 1) * P))(H0), 1 ≤ n ⊦ ⟪tree_buffer_heap_process_one#(; H0, to_delete0)⟫ ((2 ≤ n → ((del-list(to_delete0, n - 2) * P))(H0)) ∧ (n = 1 → to_delete0 = [] ∧ P(H0)))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 14:
n = m + 1, ((del-list(to_delete0, m) * P))(H0), ((del-list(to_delete, n) * P))(H), 1 ≤ n ⊦ ⟪tree_buffer_heap_process_one#(; H0, to_delete0)⟫ ((2 ≤ n → ((del-list(to_delete0, n - 2) * P))(H0)) ∧ (n = 1 → to_delete0 = [] ∧ P(H0))), n = 0

Rule argument

spec: nat name: elim-pred-c seq: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1 subst: [n, m] → [n, m]

Additional information

Used simplifier rules: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1; (elim) Used terms: n, m