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Proof step 17 from proof gc-heap-update-h (previous step)

lpt[n] = mklp(m, m4, LP_GROUP_NODES, m5), n < # lpt, key-index(m, n) ∈ gc-heap(lpt, nx, n) ⊦ # gc-heap(lpt, nx, n) = 0, gc-heap(lpt, nx, n) = ∅, key-index(m, n) = key-index(m6, n), n ∈ nx

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 18:
⊦ n ≤ # lpt → (key-index(n0, n1) ∈ gc-heap(lpt, nx, n) ↔ n1 < n ∧ ¬ n1 ∈ nx ∧ lpt[n1].ref-size = n0 ∧ lpt[n1].flags = LP_GROUP_NODES)

Rule argument

spec: <toplevel> name: gc-heap-in-h seq: ⊦ n ≤ # lpt → ( key-index(n0, n1) ∈ gc-heap(lpt, nx, n) ↔ n1 < n ∧ ¬ n1 ∈ nx ∧ lpt[n1].ref-size = n0 ∧ lpt[n1].flags = LP_GROUP_NODES) subst: [n, nx, lpt, n1, n0] → [n, nx, lpt, n, m] flags: <all paths>

Additional information

Used simplifier rules: ⊦ m < n → m ≤ n; (s)% ⊦ ¬ n < n; (s) Used terms: n, nx, lpt, n, m