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Proof step 17 from proof process-queue (previous step)

P0 = P, n0 = m, ((del-list(to_delete, m + 1) * P))(H), ((del-list(to_delete0, m) * P))(H0) ⊦ [tree_buffer_heap_process_one#(; H0, to_delete0)] ( (n0 ≥ 1 → ((del-list(to_delete0, n0 - 1) * P0))(H0)) ∧ (n0 = 0 → to_delete0 = [] ∧ ((del-list([], 0) * P0))(H0)) → (1 ≤ m → ((del-list(to_delete0, m + 1 - 2) * P))(H0)) ∧ (m = 0 → to_delete0 = [] ∧ P(H0)))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 18:
((del-list(to_delete0, m) * P))(H0), ((del-list(to_delete, m + 1) * P))(H) ⊦ [tree_buffer_heap_process_one#(; H0, to_delete0)] (((del-list(to_delete0, m - 1) * P))(H0) ∧ (m = 0 → to_delete0 = [] ∧ P(H0)) → 1 ≤ m → ((del-list(to_delete0, m + 1 - 2) * P))(H0))

Rule argument

Additional information

Used simplifier rules: sep-com: ⊦ P0 * P1 = P1 * P0; from specification heap-sep%sep-ass: ⊦ (P0 * P1) * P2 = P0 * P1 * P2; from specification heap-sep% ⊦ emp * P = P; (s)%and-com: ⊦ (P0 ∧ P1) = (P1 ∧ P0); from specification heap-sep%and-ass: ⊦ ((P0 ∧ P1) ∧ P2) = (P0 ∧ P1 ∧ P2); from specification heap-sep% ⊦ (true ∧ P) = P; (s)% ⊦ ⌜true⌝ = true; (s)% ⊦ del-list([], n) = (emp ∧ ⌜n = 0⌝ ); (s)% ⊦ n ≥ m ↔ m ≤ n; (s)