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Proof step 9 from proof lift-ex-r (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
rP(r)(mk(rs, f)), ∀ r. r ∈ rs → g(r) = a ⊦ ∃ r. a[rP(r)](mk(rs, f, g))

Rule argument

Additional information

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