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Proof step 9 from proof sep-partial-mp (previous step)

((P0 * P2 -* P1))(H1), P0(H2), P2(H0), H2 ⊥ H1, H0 ⊥ H2, H0 ⊥ H1 ⊦ P1(H0 ∪ H2 ∪ H1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ ((P0 -* P1))(H) ↔ (∀ H1. H1 ⊥ H ∧ P0(H1) → P1(H1 ∪ H))
Proof step 11:
P0(H2), P2(H0), H0 ⊥ H1, H0 ⊥ H2, H2 ⊥ H1, ∀ H0. H0 ⊥ H1 ∧ ((P0 * P2))(H0) → P1(H0 ∪ H1) ⊦ P1(H0 ∪ H2 ∪ H1)

Rule argument

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

Additional information

Used terms: H1, P1, P0 * P2