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

r =>_(H0), P(H), H0 ⊥ H, ∀ r0. (r0 ∈ rs ↔ r0 ∈ H0 ∨ r0 ∈ H) ∧ (r0 ∈ rs → f(r0) = (H0 ∪ H)[r0]) ⊦ r ∈ rs

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ r =>_ = _∃(λ o. r => o)
Proof step 11:
P(H), (_∃(λ o. r => o))(H0), H0 ⊥ H, ∀ r0. (r0 ∈ rs ↔ r0 ∈ H0 ∨ r0 ∈ H) ∧ (r0 ∈ rs → f(r0) = (H0 ∪ H)[r0]) ⊦ r ∈ rs

Rule argument

spec: maplet name: mapex seq: ⊦ r =>_ = _∃(λ o. r => o) subst: [r] → [r] flags: <all paths>

Additional information

Used terms: r