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Proof step 11 from proof lst-in-hp (previous step)

rs1 ∩ rs0 = ∅, R[rs0, cf, af], o[ls(r, x)](mk(rs1, cf, af)) ⊦ r = null, r ∈ rs0, r ∈ rs1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 12:
⊦ o[P](mk(rs, cf, af)) ↔ P(mk(rs, cf)) ∧ (∀ r. r ∈ rs → af(r) = o)
Proof step 13:
rs1 ∩ rs0 = ∅, R[rs0, cf, af], ls(r, x)(mk(rs1, cf)), ∀ r. r ∈ rs1 → af(r) = o ⊦ r = null, r ∈ rs1, r ∈ rs0

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, ls(r, x), o] flags: <all paths>

Additional information

Used terms: af, cf, rs1, ls(r, x), o