| # lpt1 = n1 + n0, lpt1[n0] = mklp(m, m0, LP_GROUP_NODES, m1), bh1 = gch, gc-heap(lpt2, log, n0) = keyset(gch), lpt3 = lpt1, n1 ≠ 0, bin-heap-inv(gch, lpt1), id-idx(lpt2, lpt1), ¬ n0 ∈ log, ∀ ki. ki ∈ gc-heap(lpt2, log, ki.idx) → ki.idx ≠ n0 ⊦ [gc_heap_insert#(key-index(m, n0); gch, lpt1)] ( bin-heap-inv(gch, lpt1) ∧ id-idx(lpt3, lpt1) ∧ keyset(gch) = keyset(bh1) ++ key-index(m, n0) → ⟪n := n0 + 1⟫ (n ≤ # lpt1 ∧ gc-heap(lpt2, log, n) = keyset(gch) ∧ id-idx(lpt2, lpt1) ∧ # lpt1 < n1 + n)) |
# lpt1 = n1 + n0, lpt1[n0] = mklp(m, m0, LP_GROUP_NODES, m1), bh1 = gch, gc-heap(lpt2, log, n0) = keyset(gch), lpt3 = lpt1, bin-heap-inv(gch, lpt1), id-idx(lpt2, lpt1), ∀ ki. ki ∈ gc-heap(lpt2, log, ki.idx) → ki.idx ≠ n0 ⊦ ∀ gch, lpt1. bin-heap-inv(gch, lpt1) ∧ id-idx(lpt3, lpt1) ∧ keyset(gch) = keyset(bh1) ++ key-index(m, n0) → ⟪n := n0 + 1⟫ (n ≤ # lpt1 ∧ gc-heap(lpt2, log, n) = keyset(gch) ∧ id-idx(lpt2, lpt1) ∧ # lpt1 < n1 + n), n1 = 0, n0 ∈ log