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Proof step 7 from proof to-vtbl-in (previous step)

v0 ∈ vols, ∀ vols0, v. # vols0 < # vols → true → (v ∈ to-vtbl(vols0) ↔ v ∈ vols0) ⊦ v ∈ to-vtbl(vols) ↔ v ∈ vols

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ v ∈ vols ↔ (∃ ebatbl, vols0. vols = vols0[v, ebatbl] ∧ ¬ v ∈ vols0)
Proof step 9:
∃ ebatbl, vols0. vols = vols0[v0, ebatbl] ∧ ¬ v0 ∈ vols0, ∀ vols0, v. # vols0 < # vols → true → (v ∈ to-vtbl(vols0) ↔ v ∈ vols0) ⊦ v ∈ to-vtbl(vols) ↔ v ∈ vols

Rule argument

spec: store, inst: volumes name: exin seq: ⊦ v ∈ vols ↔ (∃ ebatbl, vols0. vols = vols0[v, ebatbl] ∧ ¬ v ∈ vols0) subst: [vols, v] → [vols, v0] flags: <all paths>

Additional information

Used terms: vols, v0