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Proof step 32 from proof valid-recs-next-update (previous step)

# 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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 33:
# wlar = # apebs, wlar[m6] = wl-entry(m13, used), wlar[m3] = wl-entry(m12, used), apebs[m6] = mkpeb(aehdr2, avhdr1, buf2, m7, boolvar2), 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), wlar[m, wl-entry(n0, used)][m3, wl-entry(n1, erasing)][m6] = wl-entry(m11, stat), apebs[m3] = mkpeb(aehdr1, avhdr0, buf1, m8, boolvar1), m6 < # apebs, m6 < m, m3 < # apebs, m3 < m, m3 + 1 < # apebs, m6 + 1 < # apebs, m < # apebs, avhdr0.vol × avhdr0.leb ∈ recs, avhdr1.vol × avhdr1.leb ∈ recs ⊦ stat = used, avhdr1.vol × avhdr1.leb = avhdr0.vol × avhdr0.leb

Rule argument

Additional information

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