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Proof step 35 from proof bin-heap-inv-write-other (previous step)

key-index(natkey, n) ∈ keyset(kar, m) ↔ n < # lpt ∧ ¬ n ∈ nx ∧ lpt[n].ref-size = natkey ∧ lpt[n].flags = LP_GROUP_NODES, kar[m9] = key-index(natkey, n), lpt[n] = mklp(m4, m5, lpf, m6), 2exp-size(# kar), m9 < m, m9 < # kar, n < # lpt, heap-order(kar, m), no-dups-idx(kar, m), m ≤ # kar, # lpt ≤ # lpt ⊦ lpf = LP_GROUP_NODES, m6 = m9

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 36:
kar[m9] = key-index(natkey, n), lpt[n] = mklp(m4, m5, lpf, m6), 2exp-size(# kar), m9 < m, m9 < # kar, n < # lpt, heap-order(kar, m), no-dups-idx(kar, m), m ≤ # kar ⊦ lpf = LP_GROUP_NODES, m6 = m9, key-index(natkey, n) ∈ keyset(kar, m)

Rule argument

Additional information

Used simplifier rules: ⊦ mklp(n2, n3, lpf, m).flags = lpf; (s)% ⊦ mklp(n2, n3, lpf, m).ref-size = n2; (s)% ⊦ m ≤ m; (s)