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Proof step 18 from proof valid-recs-next-samerecs (previous step)

# wlar = # apebs, subarray(apebs, 0, m + 1)[m1] = mkpeb(aehdr, avhdr, buf, m5, boolvar), recs[avhdr.vol × avhdr.leb] = recovery-entry(m3, m4), subarray(wlar[m, wl-entry(m0, stat)], 0, m + 1)[m1] = wl-entry(m6, used), m < # apebs, m1 < # apebs, m1 ≤ m, ∀ ladr, m1. ladr ∈ recs ∧ recs[ladr].pnum = m1 ↔ wlar[m1].status = used ∧ m1 < m ∧ apebs[m1].vidhdr.vol = ladr.vol ∧ apebs[m1].vidhdr.leb = ladr.leb ⊦ stat = used, avhdr.vol × avhdr.leb ∈ recs ∧ m3 = m1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 19:
⊦ n + m ≤ # wlar ∧ n0 < n → subarray(wlar, m, n)[n0] = wlar[m + n0]
Proof step 20:
# wlar = # apebs, wlar[m, wl-entry(m0, stat)][0 + m1] = wl-entry(m6, used), recs[avhdr.vol × avhdr.leb] = recovery-entry(m3, m4), subarray(apebs, 0, m + 1)[m1] = mkpeb(aehdr, avhdr, buf, m5, boolvar), m1 < # apebs, m < # apebs, m1 < m + 1, m1 ≤ m, (m + 1) + 0 ≤ # wlar[m, wl-entry(m0, stat)], ∀ ladr, m1. ladr ∈ recs ∧ recs[ladr].pnum = m1 ↔ wlar[m1].status = used ∧ m1 < m ∧ apebs[m1].vidhdr.vol = ladr.vol ∧ apebs[m1].vidhdr.leb = ladr.leb ⊦ stat = used, avhdr.vol × avhdr.leb ∈ recs ∧ m3 = m1

Rule argument

spec: array-copy, inst: wlarray-base name: at-subarray seq: ⊦ n + m ≤ # wlar ∧ n0 < n → subarray(wlar, m, n)[n0] = wlar[m + n0] subst: [n0, n, m, wlar] → [m1, m + 1, 0, wlar[m, wl-entry(m0, stat)]] flags: <all paths>

Additional information

Used simplifier rules: a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ # wlar[n, wle] = # wlar; (s)% ⊦ m + 1 ≤ n ↔ m < n; (s)% ⊦ m < n + 1 ↔ ¬ n < m; (s)% ⊦ m ≤ n → (n < m ↔ false); (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat% ⊦ ¬ n < n; (s)%# wlar = n ⊦ subarray(wlar, 0, n) = wlar; (s)% ⊦ n < m → wlar[m, wle][n] = wlar[n]; (s)%# apebs = n ⊦ subarray(apebs, 0, n) = apebs; (s) Used terms: m1, m + 1, 0, wlar[m, wl-entry(m0, stat)]