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Proof step 13 from proof stability (previous step)

((P0 * {H2} ))(H0), P(H0), P1(H3), H3 ⊥ H2 ⊦ ((P1 * (P0 -⊗ P)))(H3 ∪ H2), ((P0 -⊗ P))(H2), P(H3 ∪ H2)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 14:
⊦ ((P0 -⊗ P1))(H) ↔ (∃ H0, H1. H0 ⊥ H ∧ H1 = H0 ∪ H ∧ P0(H0) ∧ P1(H1))
Proof step 15:
((P0 * {H2} ))(H0), P(H0), P1(H3), H3 ⊥ H2 ⊦ ((P1 * (P0 -⊗ P)))(H3 ∪ H2), P(H3 ∪ H2), ∃ H0, H1. H0 ⊥ H2 ∧ H1 = H0 ∪ H2 ∧ P0(H0) ∧ P(H1)

Rule argument

spec: <toplevel> name: septract seq: ⊦ ((P0 -⊗ P1))(H) ↔ (∃ H0, H1. H0 ⊥ H ∧ H1 = H0 ∪ H ∧ P0(H0) ∧ P1(H1)) subst: [H, P1, P0] → [H2, P, P0] flags: <all paths>

Additional information

Used terms: H2, P, P0