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Proof step 25 from proof prepost-create-freelist (previous step)

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)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 26:
⊦ n0 < n → subarray(lpt, m, n)[n0] = lpt[m + n0]
Proof step 27:
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)
Proof step 29:
lpt[n0] = mklp(m, m0, LP_FREE, m1), lpt[0 + n] = mklp(m2, m3, lpf, m4), n0 < # lpt, n < n0 + 1, ∀ n1. n1 < n0 ∧ lpt[n1].flags = LP_FREE ↔ n1 ∈ freelist ⊦ ¬ n0 < n ∧ lpf = LP_FREE ↔ n ∈ freelist ∨ n = n0, dups(freelist)

Rule argument

spec: array-copy, inst: gc-heap-base-index-array-base name: subarray-at seq: ⊦ n0 < n → subarray(lpt, m, n)[n0] = lpt[m + n0] subst: [n0, n, m, lpt] → [n, n0 + 1, 0, lpt] flags: <all paths>

Additional information

Used terms: n, n0 + 1, 0, lpt