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

lpt[n2] = mklp(m2, m3, lpf0, m4), lpt[n1] = mklp(m, m0, lpf, m1), n2 < # lpt, lpt[n1] = mklp(m, m0, lpf, m1) ∧ n2 ≤ # lpt → (key-index(n0, n1) ∈ gc-heap(lpt, nx, n2) ↔ n1 < n2 ∧ ¬ n1 ∈ nx ∧ m = n0 ∧ lpf = LP_GROUP_NODES) ⊦ key-index(n0, n1) ∈ gc-heap(lpt, nx, n2) ∪ (¬ n2 ∈ nx ∧ lpf0 = LP_GROUP_NODES ⊃ ∅ ++ key-index(m2, n2);∅) ↔ ¬ n2 < n1 ∧ ¬ n1 ∈ nx ∧ m = n0 ∧ lpf = LP_GROUP_NODES

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
key-index(n0, n1) ∈ gc-heap(lpt, nx, n2) ↔ n1 < n2 ∧ ¬ n1 ∈ nx ∧ m = n0 ∧ lpf = LP_GROUP_NODES, lpt[n1] = mklp(m, m0, lpf, m1), lpt[n2] = mklp(m2, m3, lpf0, m4), n2 < # lpt ⊦ key-index(n0, n1) ∈ gc-heap(lpt, nx, n2) ∪ (¬ n2 ∈ nx ∧ lpf0 = LP_GROUP_NODES ⊃ ∅ ++ key-index(m2, n2);∅) ↔ ¬ n2 < n1 ∧ ¬ n1 ∈ nx ∧ m = n0 ∧ lpf = LP_GROUP_NODES

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → m ≤ n; (s)