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Proof step 33 from proof ex-lst-shift (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 34:
⊦ R[rs, cf, af] ↔ R(mk(rs, cf, af))
Proof step 35:
rs1 ∩ rs0 = ∅, R[rs0, cf, af], xv(x)(mk(rs1, cf)), ∀ r. r ∈ rs1 → af(r) = o ⊦ o[_∃ xv](mk(rs1, cf, af)), (o[_∃ xv] * R)[rs1 ∪ rs0, cf, af]

Rule argument

spec: heap-fun, inst: cell-heap-aux-heap-aux name: apply seq: ⊦ R[rs, cf, af] ↔ R(mk(rs, cf, af)) subst: [af, cf, rs, R] → [af, cf, rs1, o[_∃ xv]] flags: <all paths>

Additional information

Used terms: af, cf, rs1, o[_∃ xv]