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Proof step 9 from proof wand-shift (previous step)

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

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(H1), P1(H), H ⊥ H0, H ⊥ H1, H1 ⊥ H0, ∀ H1. H1 ⊥ H0 ∧ P1(H1) → P2(H1 ∪ H0) ⊦ ((P0 * P2))(H ∪ H1 ∪ H0)

Rule argument

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

Additional information

Used terms: H0, P2, P1