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Proof step 24 from proof valid-recs-next-add (previous step)

# wlar = # apebs, avhdr.leb = m6, avhdr.vol = v0, v0 × m6 ∈ recs ∧ m11 = m5 ↔ stat0 = used ∧ m5 < m ∧ avhdr0.vol = v0 ∧ avhdr0.leb = m6, wlar[m5] = wl-entry(m14, stat0), recs[v0 × m6] = 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)][v0 × m6] = recovery-entry(m7, m8), subarray(wlar[m, wl-entry(m3, used)], 0, m + 1)[m5] = wl-entry(m10, stat), apebs[m5] = mkpeb(aehdr1, avhdr0, buf1, m13, boolvar1), stat = used, m < # apebs ⊦ m < m5, v × n ∈ recs, v0 × m6 ∈ recs[v × n, recovery-entry(m, m0)] ∧ m7 = m5

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 25:
# 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

Rule argument

Additional information

Used simplifier rules: lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat% ⊦ m < n ↔ ¬ n ≤ m; (ss)