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Proof step 10 from proof stability (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ P0(H0) ∧ P1(H1) ∧ H0 ⊥ H1 → ((P0 * P1))(H0 ∪ H1)
Proof step 12:
((P0 * {H2} ))(H0), P(H0), P1(H3), H3 ⊥ H2 ⊦ ((P1 * (P0 -⊗ P)))(H3 ∪ H2), P(H3 ∪ H2), P1(H3) ∧ ((P0 -⊗ P))(H2) ∧ H3 ⊥ H2

Rule argument

spec: <toplevel> name: split-union seq: ⊦ P0(H0) ∧ P1(H1) ∧ H0 ⊥ H1 → ((P0 * P1))(H0 ∪ H1) subst: [H1, H0, P1, P0] → [H2, H3, P0 -⊗ P, P1] flags: <all paths>

Additional information

Used terms: H2, H3, P0 -⊗ P, P1