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Proof step 12 from proof to-vtbl-in (previous step)

∀ 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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ v ∈ vols[v0, ebatbl] ↔ v = v0 ∨ v ∈ vols
Proof step 14:
∀ vols1, v. # vols1 < # vols0[v0, ebatbl] → true → (v ∈ to-vtbl(vols1) ↔ v ∈ vols1) ⊦ v = v0 ∨ v ∈ to-vtbl(vols0) ↔ v = v0 ∨ v ∈ vols0, v0 ∈ vols0

Rule argument

spec: store, inst: volumes name: In-insert seq: ⊦ v ∈ vols[v0, ebatbl] ↔ v = v0 ∨ v ∈ vols subst: [ebatbl, v0, vols, v] → [ebatbl, v0, vols0, v] flags: <all paths>

Additional information

Used terms: ebatbl, v0, vols0, v