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Proof step 45 from proof prepost-create-freelist (previous step)

subarray(lpt, 0, n0 + 1)[n] = mklp(m2, m3, lpf0, m4), lpt[n0] = mklp(m, m0, lpf, m1), n0 < # lpt, ∀ n. n < # subarray(lpt, 0, n0) ∧ subarray(lpt, 0, n0)[n].flags = LP_FREE ↔ n ∈ freelist ⊦ lpf = LP_FREE, dups(freelist), ¬ dups(freelist) ∧ (¬ n0 < n ∧ lpf0 = LP_FREE ↔ n ∈ freelist)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 46:
lpt[n0] = mklp(m, m0, lpf, m1), subarray(lpt, 0, n0 + 1)[n] = mklp(m2, m3, lpf0, m4), n0 < # lpt, ∀ n1. n1 < n0 ∧ lpt[n1].flags = LP_FREE ↔ n1 ∈ freelist ⊦ ¬ n0 < n ∧ lpf0 = LP_FREE ↔ n ∈ freelist, lpf = LP_FREE, dups(freelist)

Rule argument

Additional information

Used simplifier rules: c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ n + 0 = n; (s)% ⊦ n0 < n → subarray(lpt, m, n)[n0] = lpt[m + n0]; (s)% ⊦ # subarray(lpt, m, n) = n; (s)