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Proof step 6 from proof gc-heap-ididx-h (previous step)

lpt1[m0] = mklp(m, m1, lpf, m2), m0 < # lpt1, id-idx(lpt0, lpt1), ∀ lpt0, lpt1, nx. id-idx(lpt0, lpt1) ∧ m0 ≤ # lpt1 → gc-heap(lpt1, nx, m0) = gc-heap(lpt0, nx, m0) ⊦ gc-heap(lpt1, nx, m0) ∪ (¬ m0 ∈ nx ∧ lpf = LP_GROUP_NODES ⊃ ∅ ++ key-index(m, m0);∅) = gc-heap(lpt0, nx, m0 + 1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ n < # lpt → gc-heap(lpt, nx, n + 1) = gc-heap(lpt, nx, n) ∪ (¬ n ∈ nx ∧ lpt[n].flags = LP_GROUP_NODES ⊃ {key-index(lpt[n].ref-size, n)} ;∅)
Proof step 8:
lpt1[m0] = mklp(m, m1, lpf, m2), m0 < # lpt1, m0 < # lpt0, id-idx(lpt0, lpt1), ∀ lpt0, lpt1, nx. id-idx(lpt0, lpt1) ∧ m0 ≤ # lpt1 → gc-heap(lpt1, nx, m0) = gc-heap(lpt0, nx, m0) ⊦ gc-heap(lpt1, nx, m0) ∪ (¬ m0 ∈ nx ∧ lpf = LP_GROUP_NODES ⊃ ∅ ++ key-index(m, m0);∅) = gc-heap(lpt0, nx, m0) ∪ (¬ m0 ∈ nx ∧ lpt0[m0].flags = LP_GROUP_NODES ⊃ {key-index(lpt0[m0].ref-size, m0)} ;∅)

Rule argument

spec: <toplevel> name: gc-heap-rec seq: ⊦ n < # lpt → gc-heap(lpt, nx, n + 1) = gc-heap(lpt, nx, n) ∪ (¬ n ∈ nx ∧ lpt[n].flags = LP_GROUP_NODES ⊃ {key-index(lpt[n].ref-size, n)} ;∅ ) subst: [n, nx, lpt] → [m0, nx, lpt0] flags: <all paths>

Additional information

Used simplifier rules: ⊦ n < # lpt1 ∧ id-idx(lpt0, lpt1) → n < # lpt0; (ss) Used terms: m0, nx, lpt0