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Proof step 12 from proof introduce-sharing (previous step)

P0(H2 ∪ H0), P1(H1 ∪ H0), H1 ⊥ H0, H2 ⊥ H1, H2 ⊥ H0 ⊦ ((({H0} -* P0) * ({H0} -* P1) * {H0} ))(H2 ∪ H1 ∪ H0), (({H0} -* P1))(H1), (({H0} -* P0))(H2) ∧ ((({H0} -* P1) * {H0} ))(H1 ∪ H0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ ((P0 -* P1))(H) ↔ (∀ H1. H1 ⊥ H ∧ P0(H1) → P1(H1 ∪ H))
Proof step 14:
P0(H2 ∪ H0), P1(H1 ∪ H0), H2 ⊥ H0, H2 ⊥ H1, H1 ⊥ H0 ⊦ ((({H0} -* P0) * ({H0} -* P1) * {H0} ))(H2 ∪ H1 ∪ H0), ∀ H2. H2 ⊥ H1 ∧ {H0} (H2) → P1(H2 ∪ H1), (({H0} -* P0))(H2) ∧ ((({H0} -* P1) * {H0} ))(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, P1, {H0} ] flags: <all paths>

Additional information

Used terms: H1, P1, {H0}