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Proof step 9 from proof lst-in-hp (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ R[rs, cf, af] ↔ R(mk(rs, cf, af))
Proof step 11:
rs1 ∩ rs0 = ∅, R[rs0, cf, af], o[ls(r, x)](mk(rs1, cf, af)) ⊦ r = null, r ∈ rs0, r ∈ rs1

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

Additional information

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