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Proof step 10 from proof to-vtbl-in (previous step)

∀ vols1, v. # vols1 < # vols0[v0, ebatbl] → true → (v ∈ to-vtbl(vols1) ↔ v ∈ vols1) ⊦ v ∈ to-vtbl(vols0)[v0, # ebatbl] ↔ v ∈ vols0[v0, ebatbl], v0 ∈ vols0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ v ∈ vtbl[v0, n] ↔ v = v0 ∨ v ∈ vtbl
Proof step 12:
∀ vols1, v. # vols1 < # vols0[v0, ebatbl] → true → (v ∈ to-vtbl(vols1) ↔ v ∈ vols1) ⊦ v = v0 ∨ v ∈ to-vtbl(vols0) ↔ v ∈ vols0[v0, ebatbl], v0 ∈ vols0

Rule argument

spec: store, inst: vtbl name: In-insert seq: ⊦ v ∈ vtbl[v0, n] ↔ v = v0 ∨ v ∈ vtbl subst: [n, v0, vtbl, v] → [# ebatbl, v0, to-vtbl(vols0), v] flags: <all paths>

Additional information

Used terms: # ebatbl, v0, to-vtbl(vols0), v