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Proof step 23 from proof gc-heap-remove-wbufs-h (previous step)

(n0 ∈ ns ⊃ mklp(m, LEB_SIZE, lpf, m1);mklp(m, m0, lpf, m1)) = 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 ⊦ lpf0 = LP_GROUP_NODES, n0 ∈ nx, (lpf = LP_GROUP_NODES ⊃ ∅ ++ key-index(m, n0);∅) ⊆ gc-heap(lpt, nx, n0)

Heuristic if-then-else split applied rule case distinction

And obtained the following new goals

Proof step 24:
(n0 ∈ ns ⊃ mklp(m, LEB_SIZE, lpf, m1);mklp(m, m0, lpf, m1)) = 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), lpf = LP_GROUP_NODES, n0 < # lpt ⊦ lpf0 = LP_GROUP_NODES, n0 ∈ nx, ∅ ++ key-index(m, n0) ⊆ gc-heap(lpt, nx, n0)

Rule argument

pos: right 3

Additional information

Used simplifier rules: ⊦ ∅ ⊆ gchs; (s)