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Proof step 51 from proof prepost-create-freelist (previous step)

n < n0 ∧ lpf1 = LP_FREE ↔ n ∈ freelist, lpt[n0] = mklp(m, m0, lpf, m1), lpt[n] = mklp(m5, m6, lpf1, m7), n0 < # lpt, n < # lpt, n ≤ n0 ⊦ lpf1 = LP_FREE ↔ n ∈ freelist, lpf = LP_FREE, dups(freelist)

User applied rule case distinction

And closed the goal!

Rule argument

pos: right 1

Additional information

Used simplifier rules: ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m ≤ n → (n ≤ m ↔ m = n); (s)%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic% ⊦ m ≤ m; (s)%⊦ mklp(m, m0, lpf, m1) = mklp(m2, m3, lpf0, m4) ↔ m = m2 ∧ m0 = m3 ∧ lpf = lpf0 ∧ m1 = m4; (ws)