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Proof step 2 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) = (gc-heap(lpt, nx) -- key-index(n0, n)) ++ key-index(m0, n), n ∈ nx

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
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

Rule argument

Additional information

Used simplifier rules: gc-heap: ⊦ gc-heap(lpt, nx) = gc-heap(lpt, nx, # lpt);% ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ # lpt[n, lp] = # lpt; (s)