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Proof step 10 from proof process-queue (previous step)

to_delete0 = [], ((del-list(to_delete, 0) * P))(H), P(H0) ⊦ ⟪tree_buffer_heap_process_one#(; H0, to_delete0)⟫ (to_delete0 = [] ∧ P(H0))

User applied rule insert program lemma

And obtained the following new goals

Proof step 11:
((del-list(to_delete, n) * P))(H) ⊦ ⟪tree_buffer_heap_process_one#(; H, to_delete)⟫ ((n ≥ 1 → ((del-list(to_delete, n - 1) * P))(H)) ∧ (n = 0 → to_delete = [] ∧ ((del-list([], 0) * P))(H)))

Rule argument

spec: <toplevel> name: process-one seq: ((del-list(to_delete, n) * P))(H) ⊦ ⟪tree_buffer_heap_process_one#(; H, to_delete)⟫ ( (n ≥ 1 → ((del-list(to_delete, n - 1) * P))(H)) ∧ (n = 0 → to_delete = [] ∧ ((del-list([], 0) * P))(H))) subst: [n, P, to_delete, H] → [0, P, to_delete0, H0] flags: List([[1,0,0]])

Additional information

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