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Proof step 23 from proof bin-heap-inv-write-other (previous step)

lpt[n] = mklp(m0, m1, lpf0, m2), lpt[m7] = mklp(m4, m5, lpf, m6), kar[lpt[n, mklp(n0, n1, lpf1, n2)][m7].gcheapidx] = key-index(natkey, m7), keyset(bin-heap(kar, m)) = gc-heap(lpt, nx, # lpt), 2exp-size(# kar), m7 < # lpt, n < # lpt, lpt[n, mklp(n0, n1, lpf1, n2)][m7].gcheapidx < m, lpt[n, mklp(n0, n1, lpf1, n2)][m7].gcheapidx < # kar, heap-order(kar, m), no-dups-idx(kar, m), m ≤ # kar ⊦ lpf0 = LP_GROUP_NODES, m6 = lpt[n, mklp(n0, n1, lpf1, n2)][m7].gcheapidx

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 24:
kar[m9] = key-index(natkey, m7), lpt[m7] = mklp(m4, m5, lpf, m6), lpt[n] = mklp(m0, m1, lpf0, m2), lpt[n, mklp(n0, n1, lpf1, n2)][m7] = mklp(m3, m8, lpf2, m9), keyset(bin-heap(kar, m)) = gc-heap(lpt, nx, # lpt), 2exp-size(# kar), m9 < # kar, m9 < m, n < # lpt, m7 < # lpt, heap-order(kar, m), no-dups-idx(kar, m), m ≤ # kar ⊦ lpf0 = LP_GROUP_NODES, m6 = m9

Rule argument

spec: lprops name: elim seq: ⊦ ((m = lp.ref-size ∧ m0 = lp.size) ∧ lpf = lp.flags) ∧ m1 = lp.gcheapidx ↔ lp = mklp(m, m0, lpf, m1) subst: [lp, m, m0, lpf, m1] → [lpt[n, mklp(n0, n1, lpf1, n2)][m7], m3, m8, lpf2, m9]

Additional information

Used simplifier rules: ⊦ ((m = lp.ref-size ∧ m0 = lp.size) ∧ lpf = lp.flags) ∧ m1 = lp.gcheapidx ↔ lp = mklp(m, m0, lpf, m1); (elim) Used terms: lpt[n, mklp(n0, n1, lpf1, n2)][m7], m3, m8, lpf2, m9