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Proof step 16 from proof gc-heap-update-log-h (previous step)

lpt[m3] = mklp(m, m4, LP_GROUP_NODES, m5), lpt[n] = mklp(n0, n1, LP_GROUP_NODES, n2), n < # lpt, m3 < # lpt, n ∈ nx, n ≤ m3, n < m3 → gc-heap(lpt[n, mklp(m0, m1, LP_GROUP_NODES, m2)], nx, m3) = gc-heap(lpt, nx, m3) ⊦ ki ∈ gc-heap(lpt[n, mklp(m0, m1, LP_GROUP_NODES, m2)], nx, m3) ↔ ki ∈ gc-heap(lpt, nx, m3), ki = key-index(m, m3), m3 ∈ nx

User applied rule case distinction

And closed the goal!

Rule argument

pos: left 7

Additional information

Used simplifier rules: ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m ≤ n → (n ≤ m ↔ m = n); (s)