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Proof step 16 from proof adjunction (previous step)

P0(H), ∀ H. ((P0 * P1))(H) → P2(H) ⊦ ((P1 -* P2))(H)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 17:
⊦ ((P0 -* P1))(H) ↔ (∀ H1. H1 ⊥ H ∧ P0(H1) → P1(H1 ∪ H))
Proof step 18:
P0(H), ∀ H. ((P0 * P1))(H) → P2(H) ⊦ ∀ H1. H1 ⊥ H ∧ P1(H1) → P2(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, P2, P1] flags: <all paths>

Additional information

Used terms: H, P2, P1