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Proof step 20 from proof valid-recs-next-samerecs (previous step)

# wlar = # apebs, wlar[m, wl-entry(m0, stat)][0 + m1] = wl-entry(m6, used), recs[avhdr.vol × avhdr.leb] = recovery-entry(m3, m4), subarray(apebs, 0, m + 1)[m1] = mkpeb(aehdr, avhdr, buf, m5, boolvar), m1 < # apebs, m < # apebs, m1 < m + 1, m1 ≤ m, (m + 1) + 0 ≤ # wlar[m, wl-entry(m0, stat)], ∀ ladr, m1. ladr ∈ recs ∧ recs[ladr].pnum = m1 ↔ wlar[m1].status = used ∧ m1 < m ∧ apebs[m1].vidhdr.vol = ladr.vol ∧ apebs[m1].vidhdr.leb = ladr.leb ⊦ stat = used, avhdr.vol × avhdr.leb ∈ recs ∧ m3 = m1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 21:
# wlar = # apebs, apebs[m1] = mkpeb(aehdr, avhdr, buf, m5, boolvar), recs[avhdr.vol × avhdr.leb] = recovery-entry(m3, m4), wlar[m, wl-entry(m0, stat)][m1] = wl-entry(m6, used), m1 < # apebs, m < # apebs, m1 ≤ m, ∀ ladr, m1. ladr ∈ recs ∧ recs[ladr].pnum = m1 ↔ wlar[m1].status = used ∧ m1 < m ∧ apebs[m1].vidhdr.vol = ladr.vol ∧ apebs[m1].vidhdr.leb = ladr.leb ⊦ stat = used, avhdr.vol × avhdr.leb ∈ recs ∧ m3 = m1

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)