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Proof step 20 from proof embed-split (previous step)

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))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 21:
⊦ R0(Ha0) ∧ R1(Ha1) ∧ Ha0 ⊥ Ha1 → ((R0 * R1))(Ha0 ∪ Ha1)
Proof step 22:
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, f, g) ∪ mk(rs0, f, g)), a[P0](mk(rs1, f, g)) ∧ a[P1](mk(rs0, f, g)) ∧ mk(rs1, f, g) ⊥ mk(rs0, f, g)

Rule argument

spec: heap-sep, inst: heap-aux name: split-union seq: ⊦ R0(Ha0) ∧ R1(Ha1) ∧ Ha0 ⊥ Ha1 → ((R0 * R1))(Ha0 ∪ Ha1) subst: [Ha1, Ha0, R1, R0] → [mk(rs0, f, g), mk(rs1, f, g), a[P1], a[P0]] flags: <all paths>

Additional information

Used terms: mk(rs0, f, g), mk(rs1, f, g), a[P1], a[P0]