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Proof step 12 from proof gc-heap-remove-wbufs-h (previous step)

lpt[n0] = mklp(m, m0, lpf, m1), lpt.mapIndices(ns, λ lp. lp.size:= LEB_SIZE)[n0] = mklp(m2, m3, lpf0, m4), 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 ∧ lpf0 = LP_GROUP_NODES ⊃ ∅ ++ key-index(m2, n0);∅) = gc-heap(lpt, nx, n0) ∪ (¬ n0 ∈ nx ∧ lpf = LP_GROUP_NODES ⊃ ∅ ++ key-index(m, n0);∅)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ lpt.mapIndices(ns, lptfun)[n] = (n ∈ ns ∧ n < # lpt ⊃ lptfun(lpt[n]);lpt[n])
Proof step 14:
(n0 ∈ ns ∧ n0 < # lpt ⊃ lpt[n0].size:= LEB_SIZE;lpt[n0]) = mklp(m2, m3, lpf0, m4), 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 ∧ lpf0 = LP_GROUP_NODES ⊃ ∅ ++ key-index(m2, n0);∅) = gc-heap(lpt, nx, n0) ∪ (¬ n0 ∈ nx ∧ lpf = LP_GROUP_NODES ⊃ ∅ ++ key-index(m, n0);∅)

Rule argument

spec: array-indices, inst: lp-array name: mapindices-at seq: ⊦ lpt.mapIndices(ns, lptfun)[n] = (n ∈ ns ∧ n < # lpt ⊃ lptfun(lpt[n]);lpt[n]) subst: [n, lptfun, ns, lpt] → [n0, λ lp. lp.size:= LEB_SIZE, ns, lpt] flags: <all paths>

Additional information

Used terms: n0, λ lp. lp.size:= LEB_SIZE, ns, lpt