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Proof step 5 from proof valid-recs-next-add (previous step)

# wlar = # apebs, apebs[m] = mkpeb(aehdr, avidhdr(v, n, m0, m1, m4), buf, m2, boolvar), m < # apebs, ∀ ladr, m5. ladr ∈ recs ∧ recs[ladr].pnum = m5 ↔ wlar[m5].status = used ∧ m5 < m ∧ apebs[m5].vidhdr.vol = ladr.vol ∧ apebs[m5].vidhdr.leb = ladr.leb ⊦ v0 × m6 ∈ recs[v × n, recovery-entry(m, m0)] ∧ recs[v × n, recovery-entry(m, m0)][v0 × m6].pnum = m5 ↔ subarray(wlar[m, wl-entry(m3, used)], 0, m + 1)[m5].status = used ∧ ¬ m < m5 ∧ subarray(apebs, 0, m + 1)[m5].vidhdr.vol = v0 ∧ subarray(apebs, 0, m + 1)[m5].vidhdr.leb = m6, v × n ∈ recs

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 6:
# wlar = # apebs, 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), m < # apebs, ∀ ladr, m5. ladr ∈ recs ∧ recs[ladr].pnum = m5 ↔ wlar[m5].status = used ∧ m5 < m ∧ apebs[m5].vidhdr.vol = ladr.vol ∧ apebs[m5].vidhdr.leb = ladr.leb ⊦ v0 × m6 ∈ recs[v × n, recovery-entry(m, m0)] ∧ m7 = m5 ↔ subarray(wlar[m, wl-entry(m3, used)], 0, m + 1)[m5].status = used ∧ ¬ m < m5 ∧ subarray(apebs, 0, m + 1)[m5].vidhdr.vol = v0 ∧ subarray(apebs, 0, m + 1)[m5].vidhdr.leb = m6, v × n ∈ recs

Rule argument

spec: recovery-entry name: elim seq: ⊦ m = rec.pnum ∧ m0 = rec.sqn ↔ rec = recovery-entry(m, m0) subst: [rec, m, m0] → [recs[v × n, recovery-entry(m, m0)][v0 × m6], m7, m8]

Additional information

Used simplifier rules: ⊦ m = rec.pnum ∧ m0 = rec.sqn ↔ rec = recovery-entry(m, m0); (elim) Used terms: recs[v × n, recovery-entry(m, m0)][v0 × m6], m7, m8