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Proof step 4 from proof to-vtbl-in (previous step)

∀ vols0, v. # vols0 < # vols → true → (v ∈ to-vtbl(vols0) ↔ v ∈ vols0) ⊦ v ∈ to-vtbl(vols) ↔ v ∈ vols, vols = ∅

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ vols = vols0 ↔ (∀ v. (v ∈ vols ↔ v ∈ vols0) ∧ vols[v] = vols0[v])
Proof step 6:
∀ vols0, v. # vols0 < # vols → true → (v ∈ to-vtbl(vols0) ↔ v ∈ vols0) ⊦ v ∈ to-vtbl(vols) ↔ v ∈ vols, ∀ v. (v ∈ vols ↔ v ∈ ∅) ∧ vols[v] = (∅)[v]

Rule argument

spec: store, inst: volumes name: Extension seq: ⊦ vols = vols0 ↔ (∀ v. (v ∈ vols ↔ v ∈ vols0) ∧ vols[v] = vols0[v]) subst: [vols0, vols] → [∅, vols] flags: <all paths>

Additional information

Used terms: ∅, vols