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Proof step 6 from proof wand-shift (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ ((P0 -* P1))(H) ↔ (∀ H1. H1 ⊥ H ∧ P0(H1) → P1(H1 ∪ H))
Proof step 8:
((P1 -* P2))(H0), P0(H1), H1 ⊥ H0 ⊦ ∀ H2. H2 ⊥ H1 ∪ H0 ∧ P1(H2) → ((P0 * P2))(H2 ∪ H1 ∪ H0)

Rule argument

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

Additional information

Used terms: H1 ∪ H0, P0 * P2, P1