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Proof step 15 from proof valid-recs-next-samerecs (previous step)

# wlar = # apebs, wlar[m1] = wl-entry(m3, used), subarray(apebs, 0, m + 1)[m1] = mkpeb(aehdr, avhdr, buf, m5, boolvar), recs[avhdr0.vol × avhdr0.leb] = recovery-entry(m1, m4), subarray(wlar[m, wl-entry(m0, stat)], 0, m + 1)[m1] = wl-entry(m6, stat0), apebs[m1] = mkpeb(aehdr0, avhdr0, buf0, m2, boolvar0), m1 < # apebs, m1 < m, m < # apebs, m1 + 1 < # apebs, avhdr0.vol × avhdr0.leb ∈ recs ⊦ stat = used, stat0 = used ∧ avhdr.vol = avhdr0.vol ∧ avhdr.leb = avhdr0.leb

User applied rule insert rewrite lemma

And obtained the following new goals

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: ⊦ n0 < n → subarray(apebs, m, n)[n0] = apebs[m + n0]; (s)% ⊦ n + 0 = n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ n < m → wlar[m, wle][n] = wlar[n]; (s)% ⊦ # wlar[n, wle] = # wlar; (s)% ⊦ m + 1 ≤ n ↔ m < n; (s)% ⊦ m < n + 1 ↔ ¬ n < m; (s)% ⊦ n < n0 → (n0 < n ↔ false); (ss)% ⊦ wl-entry(m, stat) = wl-entry(m0, stat0) ↔ m = m0 ∧ stat = stat0; (ws)%⊦ mkpeb(aehdr, avhdr, buf, m, boolvar) = mkpeb(aehdr0, avhdr0, buf0, m0, boolvar0) ↔ aehdr = aehdr0 ∧ avhdr = avhdr0 ∧ buf = buf0 ∧ m = m0 ∧ (boolvar ↔ boolvar0); (s)% ⊦ m < n → ¬ n < m; (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 + n0 < 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)]