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Proof step 27 from proof prepost-create-freelist (previous step)

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 ⊦ ¬ n0 < n ∧ lpf = LP_FREE ↔ n ∈ freelist ∨ n = n0, n < n0 + 1, dups(freelist)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 28:
lpt[n0] = mklp(m, m0, LP_FREE, m1), subarray(lpt, 0, n0 + 1)[n] = mklp(m2, m3, lpf, m4), n0 < n, n0 < # lpt, n ∈ freelist, ∀ n1. n1 < n0 ∧ lpt[n1].flags = LP_FREE ↔ n1 ∈ freelist ⊦ n = n0, dups(freelist)

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ n < n; (s)% ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%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)