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Proof step 20 from proof bin-heap-inv-write-other-fields (previous step)

lpt[n] = mklp(m0, m1, lpf0, m2), lpt[kar[m3].idx] = mklp(m4, m5, lpf, m6), 2exp-size(# kar), m3 < # kar, n < # lpt, m3 < m, heap-order(kar, m), no-dups-idx(kar, m), m ≤ # kar, ∀ m3. m3 < m → kar[m3].idx < # lpt ∧ lpt[n, mklp(n0, n1, lpf1, m2)][kar[m3].idx].gcheapidx = m3 ⊦ kar[m3].idx < # lpt ∧ m6 = m3

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 21:
lpt[m7] = mklp(m4, m5, lpf, m6), lpt[n] = mklp(m0, m1, lpf0, m2), kar[m3] = key-index(natkey, m7), 2exp-size(# kar), m3 < m, n < # lpt, m3 < # kar, heap-order(kar, m), no-dups-idx(kar, m), m ≤ # kar, ∀ m3. m3 < m → kar[m3].idx < # lpt ∧ lpt[n, mklp(n0, n1, lpf1, m2)][kar[m3].idx].gcheapidx = m3 ⊦ m7 < # lpt ∧ m6 = m3

Rule argument

spec: key-index, inst: gc-heap-rename-gc-heap-base name: elim seq: ⊦ natkey = ki.key ∧ m = ki.idx ↔ ki = key-index(natkey, m) subst: [ki, natkey, m] → [kar[m3], natkey, m7]

Additional information

Used simplifier rules: ⊦ natkey = ki.key ∧ m = ki.idx ↔ ki = key-index(natkey, m); (elim) Used terms: kar[m3], natkey, m7