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Proof step 19 from proof valid-recs-next-add (previous step)

# wlar = # apebs, wlar[m5] = wl-entry(m14, used), apebs[m5] = mkpeb(aehdr1, avhdr0, buf1, m13, boolvar1), subarray(wlar[m, wl-entry(m3, used)], 0, m + 1)[m5] = wl-entry(m10, stat), recs[avhdr0.vol × avhdr0.leb] = recovery-entry(m5, m12), apebs[m] = mkpeb(aehdr, avidhdr(v, n, m0, m1, m4), buf, m2, boolvar), subarray(apebs, 0, m + 1)[m5] = mkpeb(aehdr0, avhdr, buf0, m9, boolvar0), m5 + 1 < # apebs, m < # apebs, m5 < # apebs, m5 < m, avhdr0.vol × avhdr0.leb ∈ recs ⊦ v × n ∈ recs, stat = 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] → [m5, m + 1, 0, wlar[m, wl-entry(m3, used)]] flags: <all paths>

Additional information

Used simplifier rules: ⊦ 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)% ⊦ n0 < n → subarray(apebs, m, n)[n0] = apebs[m + n0]; (s)% ⊦ # wlar[n, wle] = # wlar; (s)% ⊦ m + 1 ≤ n ↔ m < n; (s)% ⊦ m < n + 1 ↔ ¬ n < m; (s)% ⊦ n < n0 → (n0 < n ↔ false); (ss)%⊦ mkpeb(aehdr, avhdr, buf, m, boolvar) = mkpeb(aehdr0, avhdr0, buf0, m0, boolvar0) ↔ aehdr = aehdr0 ∧ avhdr = avhdr0 ∧ buf = buf0 ∧ m = m0 ∧ (boolvar ↔ boolvar0); (s)% ⊦ wl-entry(m, stat) = wl-entry(m0, stat0) ↔ m = m0 ∧ stat = stat0; (ws)% ⊦ 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)%# apebs = n ⊦ subarray(apebs, 0, n) = apebs; (s)%# wlar = n ⊦ subarray(wlar, 0, n) = wlar; (s)% ⊦ n + n0 < m → wlar[m, wle][n] = wlar[n]; (s) Used terms: m5, m + 1, 0, wlar[m, wl-entry(m3, used)]