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Proof step 24 from proof gc-heap-update-h (previous step)

lpt[m3] = mklp(m, m4, LP_GROUP_NODES, m5), lpt[n] = mklp(n0, n1, LP_GROUP_NODES, n2), gc-heap(lpt[n, mklp(m0, m1, LP_GROUP_NODES, m2)], nx, m3) = (gc-heap(lpt, nx, m3) -- key-index(n0, n)) ++ key-index(m0, n), n < m3, n < # lpt, m3 < # lpt, n + 1 < # lpt ⊦ m3 = n, n ∈ nx, m3 ∈ nx, ∀ ki0. ki0 ∈ (gc-heap(lpt, nx, m3) -- key-index(n0, n)) ++ key-index(m, m3) ++ key-index(m0, n) ↔ ki0 = key-index(m0, n) ∨ ki0 ∈ (gc-heap(lpt, nx, m3) -- key-index(n0, n)) ∪ ((∅ ++ key-index(m, m3)) -- key-index(n0, n))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 25:
lpt[n] = mklp(n0, n1, LP_GROUP_NODES, n2), lpt[m3] = mklp(m, m4, LP_GROUP_NODES, m5), gc-heap(lpt[n, mklp(m0, m1, LP_GROUP_NODES, m2)], nx, m3) = (gc-heap(lpt, nx, m3) -- key-index(n0, n)) ++ key-index(m0, n), n + 1 < # lpt, m3 < # lpt, n < # lpt, n < m3 ⊦ ki = key-index(m, m3) ∨ ki ≠ key-index(n0, n) ∧ ki ∈ gc-heap(lpt, nx, m3) ↔ ki ∈ (gc-heap(lpt, nx, m3) -- key-index(n0, n)) ∪ ((∅ ++ key-index(m, m3)) -- key-index(n0, n)), ki = key-index(m0, n), m3 = n, m3 ∈ nx, n ∈ nx

Rule argument

Additional information

Used simplifier rules: ⊦ ki ∈ gchs -- ki0 ↔ ki ≠ ki0 ∧ ki ∈ gchs; (s)% ⊦ ki ∈ gchs ++ ki0 ↔ ki = ki0 ∨ ki ∈ gchs; (s)