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

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
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)))

Rule argument

Additional information

Used simplifier rules: not-zero: 0 < n ⊦ (* n) ≤ m → m ≠ 0; (forward) from specification nat% ⊦ m < 1 ↔ m = 0; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ m ≠ 0 → (m < 2 ↔ m = 1); (s)