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Proof step 19 from proof lift-ex-r (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 20:
a[rP(r)](mk(rs, f, g)) ⊦ (∃ r. rP(r)(mk(rs, f))) ∧ (r0 ∈ rs → g(r0) = a)

Rule argument

Additional information

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