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

⊦ (∃ H0. H0 ⊥ H ∧ P0(H0) ∧ P1(H0 ∪ H)) ↔ ¬ ((P0 -* ¬ P1))(H)

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:
⊦ (∃ H0. H0 ⊥ H ∧ P0(H0) ∧ P1(H0 ∪ H)) ↔ ¬(∀ H1. H1 ⊥ H ∧ P0(H1) → (¬ P1)(H1 ∪ H))

Rule argument

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

Additional information

Used terms: H, ¬ P1, P0