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Proof step 8 from proof gc-heap-append-log-h (previous step)

lpt[n] = mklp(n0, n1, LP_GROUP_NODES, n2), m ≤ # lpt ⊦ key-index(n3, n4) ∈ gc-heap(lpt, n ' + nx, m) ↔ key-index(n3, n4) ≠ key-index(n0, n) ∧ key-index(n3, n4) ∈ gc-heap(lpt, nx, m), n ∈ nx

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ n ≤ # lpt → (key-index(n0, n1) ∈ gc-heap(lpt, nx, n) ↔ n1 < n ∧ ¬ n1 ∈ nx ∧ lpt[n1].ref-size = n0 ∧ lpt[n1].flags = LP_GROUP_NODES)
Proof step 10:
lpt[n] = mklp(n0, n1, LP_GROUP_NODES, n2), m ≤ # lpt ⊦ n4 < m ∧ ¬ n4 ∈ n ' + nx ∧ lpt[n4].ref-size = n3 ∧ lpt[n4].flags = LP_GROUP_NODES ↔ key-index(n3, n4) ≠ key-index(n0, n) ∧ key-index(n3, n4) ∈ gc-heap(lpt, nx, m), n ∈ nx

Rule argument

spec: <toplevel> name: gc-heap-in-h seq: ⊦ n ≤ # lpt → ( key-index(n0, n1) ∈ gc-heap(lpt, nx, n) ↔ n1 < n ∧ ¬ n1 ∈ nx ∧ lpt[n1].ref-size = n0 ∧ lpt[n1].flags = LP_GROUP_NODES) subst: [n, nx, lpt, n1, n0] → [m, n ' + nx, lpt, n4, n3] flags: <all paths>

Additional information

Used terms: m, n ' + nx, lpt, n4, n3