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Proof step 7 from proof valid-recs-next-add (previous step)

# wlar = # apebs, recs[v × n, recovery-entry(m, m0)][v0 × m6] = 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), 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 ∧ avhdr.vol = v0 ∧ avhdr.leb = m6, v × n ∈ recs

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 8:
# wlar = # apebs, 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), 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 ↔ stat = used ∧ ¬ m < m5 ∧ avhdr.vol = v0 ∧ avhdr.leb = m6, v × n ∈ recs

Rule argument

spec: wlentry name: elim-02 seq: ⊦ m = wle.ec ∧ stat = wle.status ↔ wle = wl-entry(m, stat) subst: [wle, m, stat] → [subarray(wlar[m, wl-entry(m3, used)], 0, m + 1)[m5], m10, stat]

Additional information

Used simplifier rules: ⊦ m = wle.ec ∧ stat = wle.status ↔ wle = wl-entry(m, stat); (elim) Used terms: subarray(wlar[m, wl-entry(m3, used)], 0, m + 1)[m5], m10, stat