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Proof step 12 from proof embed-split (previous step)

((P0 * P1))(mk(rs, f)), ∀ r. r ∈ rs → g(r) = a ⊦ ((a[P0] * a[P1]))(mk(rs, f, g))

User applied rule apply lemma

And obtained the following new goals

Proof step 13:
⊦ P[rs, f] ↔ P(mk(rs, f))
Proof step 14:
(P0 * P1)[rs, f] ↔ ((P0 * P1))(mk(rs, f)), ((P0 * P1))(mk(rs, f)), ∀ r. r ∈ rs → g(r) = a ⊦ ((a[P0] * a[P1]))(mk(rs, f, g))

Rule argument

spec: heap-fun name: apply seq: ⊦ P[rs, f] ↔ P(mk(rs, f)) subst: [P, rs, f] → [P0 * P1, rs, f]

Additional information

Used terms: P0 * P1, rs, f