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Proof step 19 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, freelist-cons(subarray(lpt, 0, n0), freelist) ⊦ ¬ dups(freelist + n0 ') ∧ (¬ n0 < n ∧ lpf = LP_FREE ↔ n ∈ freelist ∨ n = n0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 20:
⊦ freelist-cons(lpt, freelist) ↔ ¬ dups(freelist) ∧ (∀ n. n < # lpt ∧ lpt[n].flags = LP_FREE ↔ n ∈ freelist)
Proof step 21:
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)

Rule argument

spec: persistence-base name: freelist-cons seq: ⊦ freelist-cons(lpt, freelist) ↔ ¬ dups(freelist) ∧ (∀ n. n < # lpt ∧ lpt[n].flags = LP_FREE ↔ n ∈ freelist) subst: [freelist, lpt] → [freelist, subarray(lpt, 0, n0)] flags: <all paths>

Additional information

Used terms: freelist, subarray(lpt, 0, n0)