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Proof step 9 from proof lift-mapex (previous step)

((r => o))(H) ⊦ (_∃(λ o. r => o))(H) ∧ (∀ r0. r0 ∈ H → O(r; me)(r0) = me)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
((r => o))(H) ⊦ (∃ o. ((r => o))(H)) ∧ (r0 ∈ H → (r = r0 ⊃ me;O(r0)) = me)

Rule argument

Additional information

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