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Proof step 38 from proof embed-split (previous step)

((a[P0] * a[P1]))(mk(rs, f, g)) ⊦ a[P0 * P1](mk(rs, f, g))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 39:
⊦ ((R0 * R1))(Ha) ↔ (∃ Ha0, Ha1. Ha0 ⊥ Ha1 ∧ Ha = Ha0 ∪ Ha1 ∧ R0(Ha0) ∧ R1(Ha1))
Proof step 40:
∃ Ha0, Ha1. Ha0 ⊥ Ha1 ∧ mk(rs, f, g) = Ha0 ∪ Ha1 ∧ a[P0](Ha0) ∧ a[P1](Ha1) ⊦ a[P0 * P1](mk(rs, f, g))

Rule argument

spec: heap-sep, inst: heap-aux name: sep seq: ⊦ ((R0 * R1))(Ha) ↔ (∃ Ha0, Ha1. Ha0 ⊥ Ha1 ∧ Ha = Ha0 ∪ Ha1 ∧ R0(Ha0) ∧ R1(Ha1)) subst: [Ha, R1, R0] → [mk(rs, f, g), a[P1], a[P0]] flags: <all paths>

Additional information

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