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Proof step 26 from proof valid-recs-next-update (previous step)

# wlar = # apebs, v0 × m7 ∈ recs ∧ recs[v0 × m7].pnum = m6 ↔ wlar[m6].status = used ∧ m6 < m ∧ apebs[m6].vidhdr.vol = (v0 × m7).vol ∧ apebs[m6].vidhdr.leb = (v0 × m7).leb, apebs[m3] = mkpeb(aehdr1, avhdr0, buf1, m8, boolvar1), subarray(wlar[m, wl-entry(n0, used)][m3, wl-entry(n1, erasing)], 0, m + 1)[m6] = wl-entry(m11, stat), recs[v0 × m7] = recovery-entry(m6, m9), apebs[m] = mkpeb(aehdr, avidhdr(avhdr0.vol, avhdr0.leb, m0, m1, m5), buf, m2, boolvar), recs[avhdr0.vol × avhdr0.leb] = recovery-entry(m3, m4), subarray(apebs, 0, m + 1)[m6] = mkpeb(aehdr0, avhdr, buf0, m10, boolvar0), wlar[m3] = wl-entry(m12, used), m3 + 1 < # apebs, m < # apebs, m3 < m, m3 < # apebs, v0 × m7 ∈ recs, avhdr0.vol × avhdr0.leb ∈ recs ⊦ v0 × m7 = avhdr0.vol × avhdr0.leb, stat = used ∧ ¬ m < m6 ∧ avhdr.vol = v0 ∧ avhdr.leb = m7

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 27:
# wlar = # apebs, wlar[m6].status = used, apebs[m3] = mkpeb(aehdr1, avhdr0, buf1, m8, boolvar1), subarray(wlar[m, wl-entry(n0, used)][m3, wl-entry(n1, erasing)], 0, m + 1)[m6] = wl-entry(m11, stat), recs[apebs[m6].vidhdr.vol × apebs[m6].vidhdr.leb] = recovery-entry(m6, m9), apebs[m] = mkpeb(aehdr, avidhdr(avhdr0.vol, avhdr0.leb, m0, m1, m5), buf, m2, boolvar), recs[avhdr0.vol × avhdr0.leb] = recovery-entry(m3, m4), subarray(apebs, 0, m + 1)[m6] = mkpeb(aehdr0, avhdr, buf0, m10, boolvar0), wlar[m3] = wl-entry(m12, used), m6 + 1 < # apebs, m3 + 1 < # apebs, m < # apebs, m3 < m, m3 < # apebs, m6 < m, m6 < # apebs, apebs[m6].vidhdr.vol × apebs[m6].vidhdr.leb ∈ recs, avhdr0.vol × avhdr0.leb ∈ recs ⊦ apebs[m6].vidhdr.vol × apebs[m6].vidhdr.leb = avhdr0.vol × avhdr0.leb, stat = used ∧ avhdr.vol = apebs[m6].vidhdr.vol ∧ avhdr.leb = apebs[m6].vidhdr.leb

Rule argument

Additional information

Used simplifier rules: lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic% ⊦ m +1 = m + 1; (s)%transitivity: ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward) from specification oelem[nat-set]%lf: ⊦ m < n ∧ n < n0 → m +1 < n0; (forward) from specification nat-basic% ⊦ m < n → ¬ n < m; (s)% ⊦ recovery-entry(m, m0).pnum = m; (s)% ⊦ (v × m).leb = m; (s)% ⊦ (v × m).vol = v; (s)