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Proof step 12 from proof valid-recs-next-update (previous step)

# wlar = # apebs, subarray(wlar[m, wl-entry(n0, used)][m3, wl-entry(n1, erasing)], 0, m + 1)[m6] = wl-entry(m11, stat), recs[v × n, recovery-entry(m, m0)][v0 × m7] = recovery-entry(m6, 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), v0 × m7 = v × n, m < # apebs, v × n ∈ recs, v0 × m7 ∈ recs[v × n, recovery-entry(m, m0)], ∀ 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 ⊦ stat = used ∧ ¬ m < m6 ∧ avhdr.vol = v0 ∧ avhdr.leb = m7

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
# wlar = # apebs, apebs[m6] = mkpeb(aehdr, avidhdr(v, n, m0, m1, m5), buf, m2, boolvar), recs[v × n] = recovery-entry(m3, m4), subarray(apebs, 0, m6 + 1)[m6] = mkpeb(aehdr0, avhdr, buf0, m10, boolvar0), subarray(wlar[m6, wl-entry(n0, used)][m3, wl-entry(n1, erasing)], 0, m6 + 1)[m6] = wl-entry(m11, stat), m6 < # apebs, v × n ∈ recs, ∀ ladr, m0. ladr ∈ recs ∧ recs[ladr].pnum = m0 ↔ wlar[m0].status = used ∧ m0 < m6 ∧ apebs[m0].vidhdr.vol = ladr.vol ∧ apebs[m0].vidhdr.leb = ladr.leb ⊦ avhdr.leb = n ∧ avhdr.vol = v ∧ stat = used

Rule argument

Additional information

Used simplifier rules: ⊦ m ≤ m; (s)%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ ¬ n < n; (s)% ⊦ m < n → n ≠ 0; (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic% ⊦ ladr ∈ recs[ladr, rec]; (s)% ⊦ recovery-entry(m, m0) = recovery-entry(m1, m2) ↔ m = m1 ∧ m0 = m2; (ws)% ⊦ recs[ladr, rec][ladr] = rec; (s)% ⊦ v × m = v0 × m0 ↔ v = v0 ∧ m = m0; (ws)