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Proof step 6 from proof valid-vtbl-update-vols (previous step)

avhdr.leb = VTBL_LNUM, avhdr.vol = VTBL_VOLID, wlar[n0] = wl-entry(m0, used), apebs[n0] = mkpeb(aehdr, avhdr, buf, m, boolvar), n0 < # apebs, n0 < # wlar, v ∈ vols ⊦ is-encoded(to-vtbl(vols)[v, # vols[v]], buf) ↔ is-encoded(to-vtbl(vols), buf)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ vtbl[v] = n ∧ v ∈ vtbl → vtbl[v, n] = vtbl

Rule argument

spec: store, inst: vtbl name: ins seq: ⊦ vtbl[v] = n ∧ v ∈ vtbl → vtbl[v, n] = vtbl subst: [n, v, vtbl] → [# vols[v], v, to-vtbl(vols)] flags: <all paths>

Additional information

Used simplifier rules: ⊦ v ∈ vols → to-vtbl(vols)[v] = # vols[v]; (s)% ⊦ v ∈ to-vtbl(vols) ↔ v ∈ vols; (s) Used terms: # vols[v], v, to-vtbl(vols)