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Proof step 11 from proof gc-heap-append-log-h (previous step)

lpt[n] = mklp(n0, n1, LP_GROUP_NODES, n2), m ≤ # lpt ⊦ n4 < m ∧ n4 ≠ n ∧ ¬ n4 ∈ 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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 12:
lpt[n] = mklp(n0, n1, LP_GROUP_NODES, n2), lpt[n4] = mklp(m0, m1, lpf, m2), m ≤ # lpt ⊦ n4 < m ∧ n4 ≠ n ∧ ¬ n4 ∈ nx ∧ m0 = n3 ∧ lpf = 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: 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[n4], m0, m1, lpf, m2]

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[n4], m0, m1, lpf, m2