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Proof step 14 from proof gc-heap-append-log-h (previous step)

lpt[n4] = mklp(m0, m1, lpf, m2), lpt[n] = mklp(n0, n1, LP_GROUP_NODES, n2), m ≤ # lpt ⊦ n4 < m ∧ n4 ≠ n ∧ ¬ n4 ∈ nx ∧ m0 = n3 ∧ lpf = LP_GROUP_NODES ↔ key-index(n3, n4) ≠ key-index(n0, n) ∧ n4 < m ∧ ¬ n4 ∈ nx ∧ lpt[n4].ref-size = n3 ∧ lpt[n4].flags = LP_GROUP_NODES, n ∈ nx

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
lpt[n] = mklp(n0, n1, LP_GROUP_NODES, n2), lpt[n4] = mklp(n3, m1, LP_GROUP_NODES, m2), n4 < m, n4 < # lpt, m ≤ # lpt ⊦ n4 ≠ n ↔ key-index(n3, n4) ≠ key-index(n0, n), n ∈ nx, n4 ∈ nx

Rule argument

Additional information

Used simplifier rules: ⊦ mklp(n2, n3, lpf, m).flags = lpf; (s)% ⊦ mklp(n2, n3, lpf, m).ref-size = n2; (s)% ⊦ m < n → n ≠ 0; (s)%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic