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Proof step 11 from proof inv-create-volume (previous step)

ebm-cons(avols) ⊦ ebm-cons(avols[v, fill(mkabstractvolume(n), erased)]), v ∈ avols

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 12:
⊦ ebm-cons(avols) ↔ (∀ v. v ∈ avols → ebm-cons(avols[v]))
Proof step 13:
ebm-cons(avols) ⊦ v ∈ avols, ∀ v0. v0 ∈ avols[v, fill(mkabstractvolume(n), erased)] → ebm-cons(avols[v, fill(mkabstractvolume(n), erased)][v0])

Rule argument

spec: ebm-base name: ebm-cons-def seq: ⊦ ebm-cons(avols) ↔ (∀ v. v ∈ avols → ebm-cons(avols[v])) subst: [avols] → [avols[v, fill(mkabstractvolume(n), erased)]] flags: <all paths>

Additional information

Used terms: avols[v, fill(mkabstractvolume(n), erased)]