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Proof step 18 from proof embed-split (previous step)

rs1 ∩ rs0 = ∅, ((P0 * P1))(mk(rs1 ∪ rs0, f)), P0[rs1, f], P1[rs0, f], ∀ r. r ∈ rs1 ∪ rs0 → g(r) = a ⊦ ((a[P0] * a[P1]))(mk(rs1 ∪ rs0, f, g))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 19:
⊦ rs0 ∩ rs1 = ∅ → mk(rs0 ∪ rs1, f, g) = mk(rs0, f, g) ∪ mk(rs1, f, g)
Proof step 20:
rs1 ∩ rs0 = ∅, ((P0 * P1))(mk(rs1 ∪ rs0, f)), P1[rs0, f], P0[rs1, f], ∀ r. r ∈ rs1 ∪ rs0 → g(r) = a ⊦ ((a[P0] * a[P1]))(mk(rs1, f, g) ∪ mk(rs0, f, g))

Rule argument

spec: heap-fun, inst: heap-aux name: uni seq: ⊦ rs0 ∩ rs1 = ∅ → mk(rs0 ∪ rs1, f, g) = mk(rs0, f, g) ∪ mk(rs1, f, g) subst: [g, f, rs1, rs0] → [g, f, rs0, rs1] flags: <all paths>

Additional information

Used terms: g, f, rs0, rs1