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Proof step 4 from proof gc-heap-update-log-h (previous step)

lpt[n] = mklp(n0, n1, LP_GROUP_NODES, n2), n < # lpt, n < m3 +1, n ∈ nx, m3 +1 ≤ # lpt, ∀ lpt, n, n0, n1, n2, nx, m0, m1, m2. lpt[n] = mklp(n0, n1, LP_GROUP_NODES, n2) ∧ n < m3 ∧ n < # lpt ∧ n ∈ nx ∧ m3 ≤ # lpt → gc-heap(lpt[n, mklp(m0, m1, LP_GROUP_NODES, m2)], nx, m3) = gc-heap(lpt, nx, m3) ⊦ gc-heap(lpt[n, mklp(m0, m1, LP_GROUP_NODES, m2)], nx, m3 +1) = gc-heap(lpt, nx, m3 +1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
lpt[n] = mklp(n0, n1, LP_GROUP_NODES, n2), n < # lpt, m3 < # lpt, n ∈ nx, n ≤ m3, ∀ lpt, n, n0, n1, n2, nx, m0, m1, m2. lpt[n] = mklp(n0, n1, LP_GROUP_NODES, n2) ∧ n < m3 ∧ n < # lpt ∧ n ∈ nx ∧ m3 ≤ # lpt → gc-heap(lpt[n, mklp(m0, m1, LP_GROUP_NODES, m2)], nx, m3) = gc-heap(lpt, nx, m3) ⊦ gc-heap(lpt[n, mklp(m0, m1, LP_GROUP_NODES, m2)], nx, m3 + 1) = gc-heap(lpt, nx, m3) ∪ (¬ m3 ∈ nx ∧ lpt[m3].flags = LP_GROUP_NODES ⊃ ∅ ++ key-index(lpt[m3].ref-size, m3);∅)

Rule argument

Additional information

Used simplifier rules: gc-heap-rec: ⊦ 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)} ;∅ );% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m < n + 1 ↔ ¬ n < m; (s)% ⊦ {ki} = ∅ ++ ki; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + 1 ≤ n ↔ m < n; (s)% ⊦ m +1 = m + 1; (s)