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Proof step 13 from proof bin-heap-inv-write-other-fields (previous step)

lpt[n] = mklp(m0, m1, lpf0, m2), 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, m2)] ∧ lpt[n, mklp(n0, n1, lpf1, m2)][kar[m0].idx].gcheapidx = m0) ↔ valid-idx(kar, lpt, m)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 14:
lpt[n] = mklp(m0, m1, lpf0, m2), 2exp-size(# kar), n < # lpt, 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) ↔ valid-idx(kar, lpt, m)

Rule argument

Additional information

Used simplifier rules: ⊦ # lpt[n, lp] = # lpt; (s)