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Proof step 27 from proof prepost-init-vols-mappings (previous step)

# wlar = # apebs, avhdr0.vol × avhdr0.leb ∈ recs0 ∧ recs0[avhdr0.vol × avhdr0.leb].pnum = n0 ↔ wlar[n0].status = used ∧ n0 < # apebs ∧ apebs[n0].vidhdr.vol = (avhdr0.vol × avhdr0.leb).vol ∧ apebs[n0].vidhdr.leb = (avhdr0.vol × avhdr0.leb).leb, wlar[n0] = wl-entry(m4, used), apebs[n0] = mkpeb(aehdr0, avhdr0, buf0, m1, false), apebs[n] = mkpeb(aehdr, avhdr, buf, m, boolvar), recs0[avhdr0.vol × avhdr0.leb] = recovery-entry(m2, m3), avhdr0.valid?, n0 < # apebs, bflipset-cons(bflipset, wlar), unique-sqns(apebs), unmapped-vols(vols), valid-eraseq(wlar, q), valid-eraseq-stronger(apebs, q), valid-vtbl(apebs, vols, wlar, n), valid-wl(apebs, wlar) ⊦ n0 = n, n ∈ q, VTBL_VOLID ∈ vols, avhdr0.vol × avhdr0.leb ≠ VTBL_VOLID × VTBL_LNUM ∧ avhdr0.vol × avhdr0.leb ∈ recs0 ∧ m2 = n0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 28:
# wlar = # apebs, avhdr0.leb = VTBL_LNUM, avhdr0.vol = VTBL_VOLID, recs0[VTBL_VOLID × VTBL_LNUM] = recovery-entry(n0, m3), apebs[n] = mkpeb(aehdr, avhdr, buf, m, boolvar), apebs[n0] = mkpeb(aehdr0, avhdr0, buf0, m1, false), wlar[n0] = wl-entry(m4, used), avhdr0.valid?, n0 < # apebs, bflipset-cons(bflipset, wlar), unique-sqns(apebs), unmapped-vols(vols), valid-eraseq(wlar, q), valid-eraseq-stronger(apebs, q), valid-vtbl(apebs, vols, wlar, n), valid-wl(apebs, wlar), VTBL_VOLID × VTBL_LNUM ∈ recs0 ⊦ n0 = n, VTBL_VOLID ∈ vols, n ∈ q

Rule argument

Additional information

Used simplifier rules: lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic% ⊦ v × m = v0 × m0 ↔ v = v0 ∧ m = m0; (ws)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).vidhdr = avhdr; (s)% ⊦ wl-entry(m, stat).status = stat; (s)% ⊦ recovery-entry(m, m0).pnum = m; (s)% ⊦ (v × m).leb = m; (s)% ⊦ (v × m).vol = v; (s)