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Proof step 43 from proof prepost-init-vols-sizes (previous step)

# apebs = # wlar, avhdr.sqn = valid-sqns(VTBL_VOLID, VTBL_LNUM, apebs).max, recs[VTBL_VOLID × VTBL_LNUM] = recovery-entry(m0, m1), apebs[m0] = mkpeb(aehdr, avhdr, buf, m, boolvar), wlar[m0] = wl-entry(m2, stat), m0 < # wlar, is-encoded(to-vtbl(vols), buf), unmapped-vols(vols), valid-peb(VTBL_VOLID, VTBL_LNUM, mkpeb(aehdr, avhdr, buf, m, boolvar)), VTBL_VOLID × VTBL_LNUM ∈ recs, ∀ ladr, m. ladr ∈ recs ∧ recs[ladr].pnum = m ↔ wlar[m].status = used ∧ m < # wlar ∧ apebs[m].vidhdr.vol = ladr.vol ∧ apebs[m].vidhdr.leb = ladr.leb ⊦ stat = used, VTBL_VOLID ∈ vols

User applied rule all left

And closed the goal!

Rule argument

pos: left 11 terms: VTBL_VOLID × VTBL_LNUM, m0 abort: F discard: T computed: T

Additional information

Used simplifier rules: ⊦ (v × m).vol = v; (s)% ⊦ (v × m).leb = m; (s)% ⊦ recovery-entry(m, m0).pnum = m; (s)% ⊦ wl-entry(m, stat).status = stat; (s) Used terms: VTBL_VOLID × VTBL_LNUM, m0