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Proof step 48 from proof prepost-create-freelist (previous step)

n < n0 ∧ lpf1 = LP_FREE ↔ n ∈ freelist, lpt[n0] = mklp(m, m0, lpf, m1), subarray(lpt, 0, n0 + 1)[n] = mklp(m2, m3, lpf0, m4), lpt[n] = mklp(m5, m6, lpf1, m7), n0 < # lpt ⊦ ¬ n0 < n ∧ lpf0 = LP_FREE ↔ n ∈ freelist, lpf = LP_FREE, dups(freelist)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 49:
⊦ n0 < n → subarray(lpt, m, n)[n0] = lpt[m + n0]
Proof step 50:
n < n0 ∧ lpf1 = LP_FREE ↔ n ∈ freelist, lpt[n] = mklp(m5, m6, lpf1, m7), lpt[0 + n] = mklp(m2, m3, lpf0, m4), lpt[n0] = mklp(m, m0, lpf, m1), n0 < # lpt, n < n0 + 1 ⊦ ¬ n0 < n ∧ lpf0 = LP_FREE ↔ n ∈ freelist, lpf = LP_FREE, 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 simplifier rules: ⊦ m < n + 1 ↔ ¬ n < m; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ n < n0 → (n0 < n ↔ false); (ss)% ⊦ m < n → ¬ n < m; (s)%# lpt = n ⊦ subarray(lpt, 0, n) = lpt; (s) Used terms: n, n0 + 1, 0, lpt