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Proof step 1 from proof In-data-in (conclusion)

a ∈ st ⊦ st[a] ∈ st

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ d ∈ st ↔ (∃ a. a ∈ st ∧ st[a] = d)
Proof step 3:
a ∈ st ⊦ ∃ a0. a0 ∈ st ∧ st[a0] = st[a]

Rule argument

spec: inst: name: Data-in seq: ⊦ d ∈ st ↔ (∃ a. a ∈ st ∧ st[a] = d) subst: [st, d] → [st, st[a]] flags: rewrite, current

Additional information

Used terms: st, st[a]