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Proof step 8 from proof to-vtbl-size (previous step)

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

User applied rule apply lemma

And obtained the following new goals

Proof step 9:
⊦ v ∈ vols ↔ (∃ ebatbl, vols0. vols = vols0[v, ebatbl] ∧ ¬ v ∈ vols0)
Proof step 10:
v ∈ vols ↔ (∃ ebatbl, vols0. vols = vols0[v, ebatbl] ∧ ¬ v ∈ vols0), v ∈ vols, ∀ vols0. # vols0 < # vols → true → # to-vtbl(vols0) = # vols0 ⊦ # to-vtbl(vols) = # vols

Rule argument

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

Additional information

Used terms: v, vols