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Proof step 30 from proof valid-recs-next-update (previous step)

# wlar = # apebs, wlar[m6] = wl-entry(m13, used), wlar[m3] = wl-entry(m12, used), subarray(apebs, 0, m + 1)[m6] = mkpeb(aehdr0, avhdr, buf0, m10, boolvar0), recs[avhdr0.vol × avhdr0.leb] = recovery-entry(m3, m4), apebs[m] = mkpeb(aehdr, avidhdr(avhdr0.vol, avhdr0.leb, m0, m1, m5), buf, m2, boolvar), recs[avhdr1.vol × avhdr1.leb] = recovery-entry(m6, m9), subarray(wlar[m, wl-entry(n0, used)][m3, wl-entry(n1, erasing)], 0, m + 1)[m6] = wl-entry(m11, stat), apebs[m3] = mkpeb(aehdr1, avhdr0, buf1, m8, boolvar1), apebs[m6] = mkpeb(aehdr2, avhdr1, buf2, m7, boolvar2), m6 < # apebs, m6 < m, m3 < # apebs, m3 < m, m < # apebs, m3 + 1 < # apebs, m6 + 1 < # apebs, avhdr0.vol × avhdr0.leb ∈ recs, avhdr1.vol × avhdr1.leb ∈ recs ⊦ avhdr1.vol × avhdr1.leb = avhdr0.vol × avhdr0.leb, stat = used ∧ avhdr.vol = avhdr1.vol ∧ avhdr.leb = avhdr1.leb

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 31:
⊦ n + m ≤ # wlar ∧ n0 < n → subarray(wlar, m, n)[n0] = wlar[m + n0]
Proof step 32:
# wlar = # apebs, apebs[m6] = mkpeb(aehdr2, avhdr1, buf2, m7, boolvar2), apebs[m3] = mkpeb(aehdr1, avhdr0, buf1, m8, boolvar1), wlar[m, wl-entry(n0, used)][m3, wl-entry(n1, erasing)][0 + m6] = wl-entry(m11, stat), recs[avhdr1.vol × avhdr1.leb] = recovery-entry(m6, m9), apebs[m] = mkpeb(aehdr, avidhdr(avhdr0.vol, avhdr0.leb, m0, m1, m5), buf, m2, boolvar), recs[avhdr0.vol × avhdr0.leb] = recovery-entry(m3, m4), subarray(apebs, 0, m + 1)[m6] = mkpeb(aehdr0, avhdr, buf0, m10, boolvar0), wlar[m3] = wl-entry(m12, used), wlar[m6] = wl-entry(m13, used), m6 + 1 < # apebs, m3 + 1 < # apebs, m < # apebs, m3 < m, m3 < # apebs, m6 < m, m6 < # apebs, m6 < m + 1, avhdr1.vol × avhdr1.leb ∈ recs, avhdr0.vol × avhdr0.leb ∈ recs, (m + 1) + 0 ≤ # wlar[m, wl-entry(n0, used)][m3, wl-entry(n1, erasing)] ⊦ avhdr1.vol × avhdr1.leb = avhdr0.vol × avhdr0.leb, stat = used ∧ avhdr.vol = avhdr1.vol ∧ avhdr.leb = avhdr1.leb

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] → [m6, m + 1, 0, wlar[m, wl-entry(n0, used)][m3, wl-entry(n1, erasing)]] 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; (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)%# apebs = n ⊦ subarray(apebs, 0, n) = apebs; (s) Used terms: m6, m + 1, 0, wlar[m, wl-entry(n0, used)][m3, wl-entry(n1, erasing)]