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Proof step 17 from proof prepost-create-freelist (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 18:
lpt[n0] = mklp(m, m0, LP_FREE, m1), n0 < # lpt, freelist-cons(subarray(lpt, 0, n0), freelist) ⊦ ¬ dups(freelist + n0 ') ∧ (¬ n0 < n ∧ subarray(lpt, 0, n0 + 1)[n].flags = 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]% ⊦ n ∈ n0 ' ↔ n = n0; (s)% ⊦ n ∈ nx + nx0 ↔ n ∈ nx ∨ n ∈ nx0; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m < n + 1 ↔ ¬ n < m; (s)% ⊦ # subarray(lpt, m, n) = n; (s)