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Proof step 48 from proof bin-heap-inv-write-other (previous step)

lpt[n] = mklp(m0, m1, lpf0, m2), kar[m2] = key-index(natkey, n), keyset(bin-heap(kar, m)) = gc-heap(lpt, nx, # lpt), 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 49:
⊦ keyset(bh) = keyset(bh.ar, bh.size)
Proof step 50:
kar[m2] = key-index(natkey, n), lpt[n] = mklp(m0, m1, lpf0, m2), keyset(bin-heap(kar, m).ar, bin-heap(kar, m).size) = gc-heap(lpt, nx, # lpt), 2exp-size(# kar), m2 < # kar, n < # lpt, m2 < m, heap-order(kar, m), no-dups-idx(kar, m), m ≤ # kar ⊦ lpf0 = LP_GROUP_NODES, m6 = m2

Rule argument

spec: bin-min-heap-prepost, inst: gc-heap-rename-gc-heap-base name: keyset seq: ⊦ keyset(bh) = keyset(bh.ar, bh.size) subst: [bh] → [bin-heap(kar, m)] flags: <all paths>

Additional information

Used terms: bin-heap(kar, m)