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Proof step 6 from proof compact-local (previous step)

!(me, O, P0)(H1), !(me, O, P1)(H0), H1 ⊥ H0 ⊦ !(me, O, P0 * P1)(H1 ∪ H0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ !(id, O, P)(H) ↔ P(H) ∧ (∀ r. r ∈ H → O(r) = id)
Proof step 8:
!(me, O, P1)(H0), !(me, O, P0)(H1), H1 ⊥ H0 ⊦ ((P0 * P1))(H1 ∪ H0) ∧ (∀ r. r ∈ H1 ∪ H0 → O(r) = me)

Rule argument

spec: <toplevel> name: owned seq: ⊦ !(id, O, P)(H) ↔ P(H) ∧ (∀ r. r ∈ H → O(r) = id) subst: [H, P, O, id] → [H1 ∪ H0, P0 * P1, O, me] flags: <all paths>

Additional information

Used terms: H1 ∪ H0, P0 * P1, O, me