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Proof step 25 from proof valid-recs-next-add (previous step)

# wlar = # apebs, avhdr.vol × avhdr.leb ∈ recs ∧ m11 = m5 ↔ stat0 = used ∧ m5 < m ∧ avhdr0.vol = avhdr.vol ∧ avhdr0.leb = avhdr.leb, apebs[m5] = mkpeb(aehdr1, avhdr0, buf1, m13, boolvar1), subarray(wlar[m, wl-entry(m3, used)], 0, m + 1)[m5] = wl-entry(m10, used), recs[v × n, recovery-entry(m, m0)][avhdr.vol × avhdr.leb] = recovery-entry(m7, m8), 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), recs[avhdr.vol × avhdr.leb] = recovery-entry(m11, m12), wlar[m5] = wl-entry(m14, stat0), m < # apebs, m5 < # apebs, m5 ≤ m ⊦ v × n ∈ recs, avhdr.vol × avhdr.leb ∈ recs[v × n, recovery-entry(m, m0)] ∧ m7 = m5

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 26:
⊦ n + m ≤ # wlar ∧ n0 < n → subarray(wlar, m, n)[n0] = wlar[m + n0]
Proof step 27:
# wlar = # apebs, avhdr.vol × avhdr.leb ∈ recs ∧ m11 = m5 ↔ stat0 = used ∧ m5 < m ∧ avhdr0.vol = avhdr.vol ∧ avhdr0.leb = avhdr.leb, wlar[m5] = wl-entry(m14, stat0), recs[avhdr.vol × avhdr.leb] = recovery-entry(m11, m12), subarray(apebs, 0, m + 1)[m5] = mkpeb(aehdr0, avhdr, buf0, m9, boolvar0), apebs[m] = mkpeb(aehdr, avidhdr(v, n, m0, m1, m4), buf, m2, boolvar), recs[v × n, recovery-entry(m, m0)][avhdr.vol × avhdr.leb] = recovery-entry(m7, m8), wlar[m, wl-entry(m3, used)][0 + m5] = wl-entry(m10, used), apebs[m5] = mkpeb(aehdr1, avhdr0, buf1, m13, boolvar1), m5 < # apebs, m < # apebs, m5 < m + 1, m5 ≤ m, (m + 1) + 0 ≤ # wlar[m, wl-entry(m3, used)] ⊦ v × n ∈ recs, avhdr.vol × avhdr.leb ∈ recs[v × n, recovery-entry(m, m0)] ∧ m7 = m5

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: 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)%# apebs = n ⊦ subarray(apebs, 0, n) = apebs; (s)%# wlar = n ⊦ subarray(wlar, 0, n) = wlar; (s)% ⊦ n < m → wlar[m, wle][n] = wlar[n]; (s) Used terms: m5, m + 1, 0, wlar[m, wl-entry(m3, used)]