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Proof step 3 from proof gc-heap-update (previous step)

lpt[n] = mklp(n0, n1, LP_GROUP_NODES, n2), n < # lpt ⊦ gc-heap(lpt[n, mklp(m0, m1, LP_GROUP_NODES, m2)], nx, # lpt) = (gc-heap(lpt, nx, # lpt) -- key-index(n0, n)) ++ key-index(m0, n), n ∈ nx

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: gc-heap-update-h seq: ⊦ n < m ∧ m ≤ # lpt ∧ lpt[n] = mklp(n0, n1, LP_GROUP_NODES, n2) ∧ ¬ n ∈ nx → gc-heap(lpt[n, mklp(m0, m1, LP_GROUP_NODES, m2)], nx, m) = (gc-heap(lpt, nx, m) -- key-index(n0, n)) ++ key-index(m0, n) subst: [n0, n1, n2, m, nx, m2, m1, m0, n, lpt] → [n0, n1, n2, # lpt, nx, m2, m1, m0, n, lpt] flags: <all paths>

Additional information

Used simplifier rules: ⊦ m ≤ m; (s) Used terms: n0, n1, n2, # lpt, nx, m2, m1, m0, n, lpt