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Proof step 15 from proof lift-mapex (previous step)

!(me, O(r; me), _∃(λ o. r => o))(H) ⊦ ∃ o. ((r => o))(H)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 16:
⊦ !(id, O, P)(H) ↔ P(H) ∧ (∀ r. r ∈ H → O(r) = id)

Rule argument

spec: <toplevel> name: owned seq: ⊦ !(id, O, P)(H) ↔ P(H) ∧ (∀ r. r ∈ H → O(r) = id) subst: [H, P, O, id] → [H, _∃(λ o. r => o), O(r; me), me] flags: <all paths>

Additional information

Used simplifier rules: ⊦ (_∃ oP)(H) ↔ (∃ o. oP(o)(H)); (s) Used terms: H, _∃(λ o. r => o), O(r; me), me