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Proof step 54 from proof bin-heap-inv-write-other (previous step)

key-index(natkey, n) ∈ keyset(kar, m) ↔ key-index(natkey, n) ∈ gc-heap(lpt, nx, # lpt), lpt[n] = mklp(m0, m1, lpf0, m2), kar[m2] = key-index(natkey, n), 2exp-size(# kar), m2 < m, n < # lpt, m2 < # kar, heap-order(kar, m), no-dups-idx(kar, m), m ≤ # kar ⊦ lpf0 = LP_GROUP_NODES, m6 = m2

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 55:
⊦ 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)
Proof step 56:
key-index(natkey, n) ∈ keyset(kar, m) ↔ n < # lpt ∧ ¬ n ∈ nx ∧ lpt[n].ref-size = natkey ∧ lpt[n].flags = LP_GROUP_NODES, kar[m2] = key-index(natkey, n), lpt[n] = mklp(m0, m1, lpf0, m2), 2exp-size(# kar), m2 < # kar, n < # lpt, m2 < m, heap-order(kar, m), no-dups-idx(kar, m), m ≤ # kar, # lpt ≤ # lpt ⊦ lpf0 = LP_GROUP_NODES, m6 = m2

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] → [# lpt, nx, lpt, n, natkey] flags: <all paths>

Additional information

Used simplifier rules: ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ ¬ n < n; (s) Used terms: # lpt, nx, lpt, n, natkey