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Proof step 21 from proof prepost-create-freelist (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 22:
lpt[n0] = mklp(m, m0, LP_FREE, m1), subarray(lpt, 0, n0 + 1)[n] = mklp(m2, m3, lpf, m4), n0 < # lpt, ∀ n1. n1 < n0 ∧ lpt[n1].flags = LP_FREE ↔ n1 ∈ freelist ⊦ dups(freelist), ¬ n0 ∈ freelist ∧ (¬ n0 < n ∧ lpf = LP_FREE ↔ n ∈ freelist ∨ n = n0)

Rule argument

Additional information

Used simplifier rules: a: ⊦ (nx + nx0) + nx1 = nx + nx0 + nx1; from specification list[nat-list-set]% ⊦ dups(nx + n ') ↔ n ∈ nx ∨ dups(nx); (ws)%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)