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Proof step 11 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 ⊦ 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);∅)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 12:
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);∅)

Rule argument

spec: lprops name: elim seq: ⊦ ((m = lp.ref-size ∧ m0 = lp.size) ∧ lpf = lp.flags) ∧ m1 = lp.gcheapidx ↔ lp = mklp(m, m0, lpf, m1) subst: [lp, m, m0, lpf, m1] → [lpt.mapIndices(ns, λ lp. lp.size:= LEB_SIZE)[n0], m2, m3, lpf0, m4]

Additional information

Used simplifier rules: ⊦ ((m = lp.ref-size ∧ m0 = lp.size) ∧ lpf = lp.flags) ∧ m1 = lp.gcheapidx ↔ lp = mklp(m, m0, lpf, m1); (elim) Used terms: lpt.mapIndices(ns, λ lp. lp.size:= LEB_SIZE)[n0], m2, m3, lpf0, m4