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Proof step 10 from proof gc-heap-remove-wbufs-h (previous step)

lpt[n0] = mklp(m, m0, lpf, m1), gc-heap(lpt.mapIndices(ns, λ lp. lp.size:= LEB_SIZE), nx, n0) = gc-heap(lpt, nx, n0), n0 < # lpt, n0 < # lpt.mapIndices(ns, λ lp. lp.size:= LEB_SIZE) ⊦ gc-heap(lpt.mapIndices(ns, λ lp. lp.size:= LEB_SIZE), nx, n0) ∪ (¬ n0 ∈ nx ∧ lpt.mapIndices(ns, λ lp. lp.size:= LEB_SIZE)[n0].flags = LP_GROUP_NODES ⊃ {key-index(lpt.mapIndices(ns, λ lp. lp.size:= LEB_SIZE)[n0].ref-size, n0)} ;∅ ) = gc-heap(lpt, nx, n0) ∪ (¬ n0 ∈ nx ∧ lpf = LP_GROUP_NODES ⊃ ∅ ++ key-index(m, n0);∅)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
lpt[n0] = mklp(m, m0, lpf, m1), gc-heap(lpt.mapIndices(ns, λ lp. lp.size:= LEB_SIZE), nx, n0) = gc-heap(lpt, nx, n0), n0 < # lpt ⊦ gc-heap(lpt, nx, n0) ∪ (¬ n0 ∈ nx ∧ lpt.mapIndices(ns, λ lp. lp.size:= LEB_SIZE)[n0].flags = LP_GROUP_NODES ⊃ ∅ ++ key-index(lpt.mapIndices(ns, λ lp. lp.size:= LEB_SIZE)[n0].ref-size, n0) ;∅ ) = gc-heap(lpt, nx, n0) ∪ (¬ n0 ∈ nx ∧ lpf = LP_GROUP_NODES ⊃ ∅ ++ key-index(m, n0);∅)

Rule argument

Additional information

Used simplifier rules: ⊦ # lpt.mapIndices(ns, lptfun) = # lpt; (s)% ⊦ {ki} = ∅ ++ ki; (s)