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Proof step 10 from proof ex-lst-shift (previous step)

rs1 ∩ rs0 = ∅, R[rs0, cf, af], (_∃ xv)(mk(rs1, cf)), ∀ r. r ∈ rs1 → af(r) = o ⊦ ∃ x. (o[xv(x)] * R)[rs1 ∪ rs0, cf, af]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ (_∃ xv)(mk(rs, cf)) ↔ (∃ x. xv(x)(mk(rs, cf)))
Proof step 12:
rs1 ∩ rs0 = ∅, R[rs0, cf, af], ∀ r. r ∈ rs1 → af(r) = o, ∃ x. xv(x)(mk(rs1, cf)) ⊦ ∃ x. (o[xv(x)] * R)[rs1 ∪ rs0, cf, af]

Rule argument

spec: <toplevel> name: ex-lst seq: ⊦ (_∃ xv)(mk(rs, cf)) ↔ (∃ x. xv(x)(mk(rs, cf))) subst: [cf, rs, xv] → [cf, rs1, xv] flags: <all paths>

Additional information

Used terms: cf, rs1, xv