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Proof step 12 from proof lift-ex-o (previous step)

(_∃ oP)(mk(rs, f)), ∀ r. r ∈ rs → g(r) = a ⊦ ∃ o. a[oP(o)](mk(rs, f, g))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
oP(o)(mk(rs, f)), ∀ r. r ∈ rs → g(r) = a ⊦ ∃ o. a[oP(o)](mk(rs, f, g))

Rule argument

Additional information

Used simplifier rules: ⊦ (_∃ oP)(H) ↔ (∃ o. oP(o)(H)); (s)