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Proof step 21 from proof cf-map-unknown (previous step)

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)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 22:
⊦ o[P](mk(rs, cf, af)) ↔ P(mk(rs, cf)) ∧ (∀ r. r ∈ rs → af(r) = o)
Proof step 23:
cf(r) = a × r0, rs1 ∩ rs0 = ∅, ((r => ce))(mk(rs1, cf)), R[rs0, cf, af], ∀ r. r ∈ rs1 → af(r) = o ⊦ (o[r => a × r0] * R)[rs1 ∪ rs0, cf, af], ((r => a × r0))(mk(rs1, cf)) ∧ (r1 ∈ rs1 → af(r1) = o)

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, r => ce, o] flags: <all paths>

Additional information

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