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Proof step 7 from proof ex-lst-shift (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ o[P](mk(rs, cf, af)) ↔ P(mk(rs, cf)) ∧ (∀ r. r ∈ rs → af(r) = o)
Proof step 9:
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]

Rule argument

spec: embed-aux, inst: cell-heap-aux name: lift-aux seq: ⊦ o[P](mk(rs, cf, af)) ↔ P(mk(rs, cf)) ∧ (∀ r. r ∈ rs → af(r) = o) subst: [af, cf, rs, P, o] → [af, cf, rs1, _∃ xv, o] flags: <all paths>

Additional information

Used terms: af, cf, rs1, _∃ xv, o