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Proof step 22 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 ⊦ dups(freelist), ¬ n0 ∈ freelist ∧ (¬ n0 < n ∧ lpf = LP_FREE ↔ n ∈ freelist ∨ n = n0)

User applied rule case distinction

And obtained the following new goals

Proof step 23:
subarray(lpt, 0, n0 + 1)[n] = mklp(m2, m3, lpf, m4), lpt[n0] = mklp(m, m0, LP_FREE, m1), n0 < # lpt, n0 ∈ freelist, ∀ n1. n1 < n0 ∧ lpt[n1].flags = LP_FREE ↔ n1 ∈ freelist ⊦ dups(freelist)
Proof step 25:
subarray(lpt, 0, n0 + 1)[n] = mklp(m2, m3, lpf, m4), lpt[n0] = mklp(m, m0, LP_FREE, m1), n0 < # lpt, ∀ n1. n1 < n0 ∧ lpt[n1].flags = LP_FREE ↔ n1 ∈ freelist ⊦ ¬ n0 < n ∧ lpf = LP_FREE ↔ n ∈ freelist ∨ n = n0, dups(freelist)

Rule argument

pos: right 2

Proof step 22 from proof prepost-create-freelist (previous step)

User applied rule case distinction

And obtained the following new goals

Rule argument

Additional information