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Proof step 27 from proof introduce-sharing (previous step)

(((P -* P1) * P))(H0), ((P -* P0))(H1), H1 ⊥ H0 ⊦ ((P0 ⊗ P1))(H1 ∪ H0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 28:
⊦ ((P0 * P1))(H) ↔ (∃ H0, H1. H0 ⊥ H1 ∧ H = H0 ∪ H1 ∧ P0(H0) ∧ P1(H1))
Proof step 29:
((P -* P0))(H1), H1 ⊥ H0, ∃ H2, H1. H2 ⊥ H1 ∧ H0 = H2 ∪ H1 ∧ ((P -* P1))(H2) ∧ P(H1) ⊦ ((P0 ⊗ P1))(H1 ∪ H0)

Rule argument

spec: <toplevel> name: sep seq: ⊦ ((P0 * P1))(H) ↔ (∃ H0, H1. H0 ⊥ H1 ∧ H = H0 ∪ H1 ∧ P0(H0) ∧ P1(H1)) subst: [H, P1, P0] → [H0, P, P -* P1] flags: <all paths>

Additional information

Used terms: H0, P, P -* P1