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Proof step 43 from proof valid-recs-next-update (previous step)

# wlar = # apebs, wlar[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), apebs[m6] = mkpeb(aehdr0, avhdr, buf0, m10, boolvar0), avhdr.vol × avhdr.leb = v × n, m6 < m, m < # apebs, m6 < # apebs, m6 + 1 < # apebs, v × n ∈ recs, ∀ 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 ⊦ m6 = m3, m6 = m, 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 44:
# wlar = # apebs, apebs[m8] = mkpeb(aehdr, avidhdr(avhdr.vol, avhdr.leb, m0, m1, m5), buf, m2, boolvar), recs[avhdr.vol × avhdr.leb] = recovery-entry(m3, m4), apebs[m6] = mkpeb(aehdr0, avhdr, buf0, m10, boolvar0), wlar[m6] = wl-entry(m11, used), m6 < # apebs, m6 + 1 < # apebs, m6 < m8, m8 < # apebs, avhdr.vol × avhdr.leb ∈ recs, ∀ ladr, m6. ladr ∈ recs ∧ recs[ladr].pnum = m6 ↔ wlar[m6].status = used ∧ m6 < m8 ∧ apebs[m6].vidhdr.vol = ladr.vol ∧ apebs[m6].vidhdr.leb = ladr.leb ⊦ m6 = m3, m6 = m8

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (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)