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Proof step 11 from proof bin-heap-inv-write-other (previous step)

lpt[n] = mklp(m0, m1, lpf0, m2), keyset(bin-heap(kar, m)) = gc-heap(lpt, nx, # lpt), 2exp-size(# kar), n < # lpt, heap-order(kar, m), no-dups-idx(kar, m), m ≤ # kar ⊦ valid-idx(kar, lpt[n, mklp(n0, n1, lpf1, n2)], m) ↔ valid-idx(kar, lpt, m), lpf0 = LP_GROUP_NODES

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 12:
⊦ valid-idx(kar, lpt, n) ↔ n ≤ # kar ∧ (∀ m. m < n → kar[m].idx < # lpt ∧ lpt[kar[m].idx].gcheapidx = m)
Proof step 13:
lpt[n] = mklp(m0, m1, lpf0, m2), keyset(bin-heap(kar, m)) = gc-heap(lpt, nx, # lpt), 2exp-size(# kar), n < # lpt, heap-order(kar, m), no-dups-idx(kar, m), m ≤ # kar ⊦ m ≤ # kar ∧ (∀ m0. m0 < m → kar[m0].idx < # lpt[n, mklp(n0, n1, lpf1, n2)] ∧ lpt[n, mklp(n0, n1, lpf1, n2)][kar[m0].idx].gcheapidx = m0) ↔ valid-idx(kar, lpt, m), lpf0 = LP_GROUP_NODES

Rule argument

spec: bin-min-heap-inv, inst: gc-heap-rename-gc-heap-base name: valid-idx seq: ⊦ valid-idx(kar, lpt, n) ↔ n ≤ # kar ∧ (∀ m. m < n → kar[m].idx < # lpt ∧ lpt[kar[m].idx].gcheapidx = m) subst: [n, lpt, kar] → [m, lpt[n, mklp(n0, n1, lpf1, n2)], kar] flags: <all paths>

Additional information

Used terms: m, lpt[n, mklp(n0, n1, lpf1, n2)], kar