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Proof step 37 from proof valid-recs-next-update (previous step)

# wlar = # apebs, wlar[m, wl-entry(n0, used)][m3, wl-entry(n1, erasing)][0 + m6] = wl-entry(m11, used), recs[v × n, recovery-entry(m, m0)][avhdr.vol × avhdr.leb] = recovery-entry(m8, m9), apebs[m] = mkpeb(aehdr, avidhdr(v, n, m0, m1, m5), buf, m2, boolvar), recs[v × n] = recovery-entry(m3, m4), subarray(apebs, 0, m + 1)[m6] = mkpeb(aehdr0, avhdr, buf0, m10, boolvar0), m6 < # apebs, m < # apebs, m6 < m + 1, v × n ∈ recs, m6 ≤ m, (m + 1) + 0 ≤ # wlar[m, wl-entry(n0, used)][m3, wl-entry(n1, erasing)], ∀ ladr, m6. ladr ∈ recs ∧ recs[ladr].pnum = m6 ↔ wlar[m6].status = used ∧ m6 < m ∧ apebs[m6].vidhdr.vol = ladr.vol ∧ apebs[m6].vidhdr.leb = ladr.leb ⊦ avhdr.vol × avhdr.leb ∈ recs[v × n, recovery-entry(m, m0)] ∧ m8 = m6

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 38:
# wlar = # apebs, apebs[m6] = mkpeb(aehdr0, avhdr, buf0, m10, boolvar0), recs[v × n] = recovery-entry(m3, m4), apebs[m] = mkpeb(aehdr, avidhdr(v, n, m0, m1, m5), buf, m2, boolvar), recs[v × n, recovery-entry(m, m0)][avhdr.vol × avhdr.leb] = recovery-entry(m8, m9), wlar[m, wl-entry(n0, used)][m3, wl-entry(n1, erasing)][m6] = wl-entry(m11, used), m6 < # apebs, m < # apebs, v × n ∈ recs, m6 ≤ m, ∀ ladr, m6. ladr ∈ recs ∧ recs[ladr].pnum = m6 ↔ wlar[m6].status = used ∧ m6 < m ∧ apebs[m6].vidhdr.vol = ladr.vol ∧ apebs[m6].vidhdr.leb = ladr.leb ⊦ avhdr.vol × avhdr.leb ∈ recs[v × n, recovery-entry(m, m0)] ∧ m8 = m6

Rule argument

Additional information

Used simplifier rules: ⊦ m ≤ n → (n < m ↔ false); (s)% ⊦ 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)