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Proof step 18 from proof introduce-sharing (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 19:
⊦ ((P0 -* P1))(H) ↔ (∀ H1. H1 ⊥ H ∧ P0(H1) → P1(H1 ∪ H))
Proof step 20:
(({H0} -* P1))(H1), P0(H2 ∪ H0), P1(H1 ∪ H0), H2 ⊥ H0, H2 ⊥ H1, H1 ⊥ H0 ⊦ ((({H0} -* P0) * ({H0} -* P1) * {H0} ))(H2 ∪ H1 ∪ H0), ∀ H1. H1 ⊥ H2 ∧ {H0} (H1) → P0(H1 ∪ H2)

Rule argument

spec: <toplevel> name: wand seq: ⊦ ((P0 -* P1))(H) ↔ (∀ H1. H1 ⊥ H ∧ P0(H1) → P1(H1 ∪ H)) subst: [H, P1, P0] → [H2, P0, {H0} ] flags: <all paths>

Additional information

Used terms: H2, P0, {H0}