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Proof step 5 from proof ex1-shiftw (previous step)

∀ H1. H1 ⊥ H ∧ (_∃ rP)(H1) → P(H1 ∪ H) ⊦ ((rP(r) -* P))(H)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
∀ H0. H0 ⊥ H ∧ (∃ r. rP(r)(H0)) → P(H0 ∪ H) ⊦ ((rP(r) -* P))(H)

Rule argument

Additional information

Used simplifier rules: ex1: ⊦ (_∃ rP)(H) ↔ (∃ r. rP(r)(H));