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Proof step 3 from proof lst-in-hp (previous step)

(o[_∃(λ x. ls(r, x))] * R)[rs, cf, af] ⊦ r = null, r ∈ rs

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ (o[_∃ xv] * R)[rs, cf, af] ↔ (∃ x. (o[xv(x)] * R)[rs, cf, af])
Proof step 5:
∃ x. (o[ls(r, x)] * R)[rs, cf, af] ⊦ r = null, r ∈ rs

Rule argument

spec: <toplevel> name: ex-lst-shift seq: ⊦ (o[_∃ xv] * R)[rs, cf, af] ↔ (∃ x. (o[xv(x)] * R)[rs, cf, af]) subst: [af, cf, rs, R, xv, o] → [af, cf, rs, R, λ x. ls(r, x), o] flags: <all paths>

Additional information

Used terms: af, cf, rs, R, λ x. ls(r, x), o