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Proof step 15 from proof embed-split (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 16:
⊦ (P0 * P1)[rs, f] ↔ (∃ rs0, rs1. rs0 ∪ rs1 = rs ∧ rs0 ∩ rs1 = ∅ ∧ P0[rs0, f] ∧ P1[rs1, f])
Proof step 17:
((P0 * P1))(mk(rs, f)), ∀ r. r ∈ rs → g(r) = a, ∃ rs0, rs1. rs0 ∪ rs1 = rs ∧ rs0 ∩ rs1 = ∅ ∧ P0[rs0, f] ∧ P1[rs1, f] ⊦ ((a[P0] * a[P1]))(mk(rs, f, g))

Rule argument

spec: heap-fun name: sep seq: ⊦ (P0 * P1)[rs, f] ↔ (∃ rs0, rs1. rs0 ∪ rs1 = rs ∧ rs0 ∩ rs1 = ∅ ∧ P0[rs0, f] ∧ P1[rs1, f]) subst: [f, rs, P1, P0] → [f, rs, P1, P0] flags: <all paths>

Additional information

Used terms: f, rs, P1, P0