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Proof step 19 from proof cf-map-unknown (previous step)

cf(r) = a × r0, rs1 ∩ rs0 = ∅, R[rs0, cf, af], o[r => ce][rs1, cf, af] ⊦ (o[r => a × r0] * R)[rs1 ∪ rs0, cf, af], ((r => a × r0))(mk(rs1, cf)) ∧ (r1 ∈ rs1 → af(r1) = o)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 20:
⊦ R[rs, cf, af] ↔ R(mk(rs, cf, af))
Proof step 21:
cf(r) = a × r0, rs1 ∩ rs0 = ∅, o[r => ce](mk(rs1, cf, af)), R[rs0, cf, af] ⊦ (o[r => a × r0] * R)[rs1 ∪ rs0, cf, af], ((r => a × r0))(mk(rs1, cf)) ∧ (r1 ∈ rs1 → af(r1) = o)

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[r => ce]] flags: <all paths>

Additional information

Used terms: af, cf, rs1, o[r => ce]