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Proof step 13 from proof wand-shift (previous step)

P0(H1), P1(H), P2(H ∪ H0), H ⊥ H0, H ⊥ H1, H1 ⊥ H0 ⊦ ((P0 * P2))(H ∪ H1 ∪ H0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 14:
⊦ ((P0 * P1))(H) ↔ (∃ H0, H1. H0 ⊥ H1 ∧ H = H0 ∪ H1 ∧ P0(H0) ∧ P1(H1))
Proof step 15:
P0(H1), P1(H), P2(H ∪ H0), H1 ⊥ H0, H ⊥ H1, H ⊥ H0 ⊦ ∃ H3, H2. H3 ⊥ H2 ∧ H ∪ H1 ∪ H0 = H3 ∪ H2 ∧ P0(H3) ∧ P2(H2)

Rule argument

spec: <toplevel> name: sep seq: ⊦ ((P0 * P1))(H) ↔ (∃ H0, H1. H0 ⊥ H1 ∧ H = H0 ∪ H1 ∧ P0(H0) ∧ P1(H1)) subst: [H, P1, P0] → [H ∪ H1 ∪ H0, P2, P0] flags: <all paths>

Additional information

Used terms: H ∪ H1 ∪ H0, P2, P0