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Proof step 9 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} -* P0))(H2) ∧ ((({H0} -* P1) * {H0} ))(H1 ∪ H0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ P0(H0) ∧ P1(H1) ∧ H0 ⊥ H1 → ((P0 * P1))(H0 ∪ H1)
Proof step 11:
P0(H2 ∪ H0), P1(H1 ∪ H0), H2 ⊥ H0, H2 ⊥ H1, H1 ⊥ H0 ⊦ ((({H0} -* P0) * ({H0} -* P1) * {H0} ))(H2 ∪ H1 ∪ H0), (({H0} -* P0))(H2) ∧ ((({H0} -* P1) * {H0} ))(H1 ∪ H0), (({H0} -* P1))(H1) ∧ {H0} (H0) ∧ H1 ⊥ H0
Proof step 17:
(({H0} -* P1))(H1), P0(H2 ∪ H0), P1(H1 ∪ H0), {H0} (H0), H2 ⊥ H0, H2 ⊥ H1, H1 ⊥ H0 ⊦ ((({H0} -* P0) * ({H0} -* P1) * {H0} ))(H2 ∪ H1 ∪ H0), (({H0} -* P0))(H2) ∧ true

Rule argument

spec: <toplevel> name: split-union seq: ⊦ P0(H0) ∧ P1(H1) ∧ H0 ⊥ H1 → ((P0 * P1))(H0 ∪ H1) subst: [H1, H0, P1, P0] → [H0, H1, {H0} , {H0} -* P1] flags: <all paths>

Additional information

Used terms: H0, H1, {H0} , {H0} -* P1