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Proof step 20 from proof compact-local (previous step)

P0(H1), P1(H0), H1 ⊥ H0, ∀ r. r ∈ H1 ∨ r ∈ H0 → O(r) = me ⊦ ((!(me, O, P0) * !(me, O, P1)))(H1 ∪ H0), !(me, O, P0)(H1) ∧ !(me, O, P1)(H0)

User applied rule case distinction

And obtained the following new goals

Proof step 21:
P0(H1), P1(H0), H1 ⊥ H0, ∀ r. r ∈ H1 ∨ r ∈ H0 → O(r) = me ⊦ !(me, O, P0)(H1), ((!(me, O, P0) * !(me, O, P1)))(H1 ∪ H0)
Proof step 25:
P0(H1), P1(H0), H1 ⊥ H0, ∀ r. r ∈ H1 ∨ r ∈ H0 → O(r) = me ⊦ !(me, O, P1)(H0), ((!(me, O, P0) * !(me, O, P1)))(H1 ∪ H0)

Rule argument

pos: right 2

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