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

lpt[n, mklp(m0, m1, LP_FREE, m2)][m3] = mklp(m6, m7, lpf0, m8), lpt[m3] = mklp(m, m4, lpf, m5), lpt[n] = mklp(n0, n1, LP_GROUP_NODES, n2), gc-heap(lpt[n, mklp(m0, m1, LP_FREE, m2)], nx, m3) = gc-heap(lpt, nx, m3) -- key-index(n0, n), n < # lpt, m3 < # lpt, n ≤ m3 ⊦ gc-heap(lpt[n, mklp(m0, m1, LP_FREE, m2)], nx, m3) ∪ (¬ m3 ∈ nx ∧ lpf0 = LP_GROUP_NODES ⊃ ∅ ++ key-index(m, m3);∅) = (gc-heap(lpt, nx, m3) -- key-index(n0, n)) ∪ ((¬ m3 ∈ nx ∧ lpf = LP_GROUP_NODES ⊃ ∅ ++ key-index(m, m3);∅) -- key-index(n0, n)), n ∈ nx

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 17:
lpt[n] = mklp(n0, n1, LP_GROUP_NODES, n2), lpt[m3] = mklp(m, m4, lpf, m5), lpt[n, mklp(m0, m1, LP_FREE, m2)][m3] = mklp(m6, m7, lpf0, m8), gc-heap(lpt[n, mklp(m0, m1, LP_FREE, m2)], nx, m3) = gc-heap(lpt, nx, m3) -- key-index(n0, n), m3 < # lpt, n < # lpt, n ≤ m3 ⊦ (gc-heap(lpt, nx, m3) -- key-index(n0, n)) ∪ (¬ m3 ∈ nx ∧ lpf0 = LP_GROUP_NODES ⊃ ∅ ++ key-index(m, m3);∅) = (gc-heap(lpt, nx, m3) -- key-index(n0, n)) ∪ ((¬ m3 ∈ nx ∧ lpf = LP_GROUP_NODES ⊃ ∅ ++ key-index(m, m3);∅) -- key-index(n0, n)), n ∈ nx

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

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