[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 3 from proof refine-add (previous step)

xs_len = # xs, ((ls(rxs, xs) * ls(rys, ys) * del-list(to_delete, n)))(H), # xs < h0, n + # xs ≤ h0, n ≤ # xs + # ys, ys = [] ∨ # ys = h0 ⊦ ⟪tree_buffer_heap_add#(a, h0; H, rxs, rys, xs_len, to_delete)⟫ ⟨xs_len0 := # xs; caterpillar_add#(a, h0; xs, xs_len0, ys)⟩ ∃ n. ((ls(rxs, xs) * ls(rys, ys) * del-list(to_delete, n)))(H) ∧ n ≤ # xs + # ys ∧ n + # xs ≤ h0 ∧ xs_len = xs_len0

Heuristic nonrecursive calls applied rule call right

And obtained the following new goals

Proof step 4:
h = h0, xs_len = # xs, ((ls(rxs, xs) * ls(rys, ys) * del-list(to_delete, n)))(H), # xs < h0, n ≤ # xs + # ys, n + # xs ≤ h0, ys = [] ∨ # ys = h0 ⊦ ⟪tree_buffer_heap_process_queue#(; H, to_delete); choose r with ¬ r ∈ H ∧ r ≠ null in {H := H ++ r; H[r].val := a; H[r].nxt := rxs; if xs_len + 1 = h then {if rys ≠ null then to_delete := rys + to_delete; rys := r; xs_len := 0; rxs := null} else {rxs := r; xs_len := 1 + xs_len}}⟫ ⟨xs_len0 := # xs; caterpillar_add#(a, h0; xs, xs_len0, ys)⟩ ∃ n. ((ls(rxs, xs) * ls(rys, ys) * del-list(to_delete, n)))(H) ∧ n ≤ # xs + # ys ∧ n + # xs ≤ h0 ∧ xs_len = xs_len0

Rule argument

pos: right 1

Additional information

Used simplifier rules: tree_buffer_heap_add#(a, h; H, rxs, rys, xs_len, to_delete) {tree_buffer_heap_process_queue#(; H, to_delete); choose r with ¬ r ∈ H ∧ r ≠ null in {H := H ++ r; H[r].val := a; H[r].nxt := rxs; if xs_len + 1 = h then {if rys ≠ null then to_delete := rys + to_delete; rys := r; xs_len := 0; rxs := null} else {rxs := r; xs_len := 1 + xs_len}} };